There’s a detailed description of the mosaic in Meyboom’s The Nile Mosaic of Palestrina, and in this answer I will be mostly quoting from this work.
Organization of the mosaic
It has always been agreed that there is an essential difference in content between the upper and lower half of the mosaic so that actually consists of two parts. In the upper part we see a waste land consisting of sand, rocks and water, populated by a large number of wild African animals, mostly with their names inscribed, which are hunted by negroes. In the lower part we see various scenes from Egypt, such as banquets, religious ceremonies, hunting parties and fishermen, scattered among temples and dwellings of various kinds, all set in a landscape which abounds in water. It is, therefore, generally assumed that the lower part represents Egypt and the upper part Nubia, in the way of a pictorial map of the Nile valley rendered in a bird’s eye view and with the south at the top as was the customer in ancient maps.
P. G. P. Meyboom (1995). The Nile Mosaic of Palestrina: Early Evidence of Egyptian Religion in Italy, p. 43. Leiden: E. J. Brill.
A notable feature of the mosaic is that the animals in the upper (Nubian) landscape are labelled in Greek, suggesting that they would be expected to be unfamiliar to the audience, while the animals in the lower (Egyptian) landscape are unlabelled, suggesting that they would be familiar to the audience. The Egyptian animals are portrayed more realistically, suggesting that the artist was able to portray them from life: there’s no difficulty in recognizing the Nile crocodiles in B8–C8, or the hippopotami in B7–D7. Accordingly I’ve only covered the upper parts (rows 0–4) of the mosaic.
History of the mosaic
The mosaic “originally covered the floor of a partly artificial grotto in the mountainside on which the town of Praeneste was built” (p. 8) and probably dates to the first century BCE, though this is very uncertain. In the Christian era, the grotto was incorporated into the palace of the Archbishop of Palestrina. However,
Between 1624 and 1626 most of the mosaic was cut into sections and removed piecemeal, without a plan of the original being made, and was transported to Rome where it came into the possession of the Cardinal Francesco Barberini. Around 1630 watercolour copies were made of the various pieces for Cassiano dal Pozzo, a man with a strong antiquarian interest and one of the founders of the Accademia dei Lincei. Somewhat later the pieces were repaired by Giovanni Battista Calandra, the head of the mosaic works of St. Peter’s, and in 1640 they were returned to Palestrina. Upon arrival, however, the packing boxes were crushed and the pieces badly damaged. Calandra again restored them with the help of the Dal Pozzo copies, and reassembled them in an apse at the back of the hall in the Barberini Palace, possibly with the inclusion of fragments which had remained on the site. [Meyboom, p. 3]
This history means that there is some uncertainty about the accuracy of the reconstruction. Some parts appearing in the dal Pozzo copies have disappeared from the mosaic, and other parts differ significantly from their appearance in the copies. For example, the centaur at I2 was originally above the snake at C2:
C1, D1, G1, H0, H1 Meyboom identifies the birds as herons (p. 23).
H1 There’s a peacock below the hunting dog. This is hard to make out on the mosaic, but clear on the dal Pozzo copy:
G1 The back legs of an animal disappear behind an outcrop. Meyboom says:
From the Dal Pozzo copy of this section it would seem that the artist had begun to sketch an elephant on the right-hand side of the rock, where there is now sky, but did not finish it, probably because too little of the original was left. [p. 23]
C2 A large striped snake, perhaps a rock python, that has caught a bird.
Pliny† and Aelian‡ relate a story that large snakes catch and gulp down birds passing over them, even though they are flying high and fast. A similar story must be represented here. […] Aethiopia was notorious for its large snakes, which are rock pythons. The capture of an Aethiopian giant snake in the reign of Ptolemy II is described by Agatharchides of Cnidos§. [Meyboom, p. 20]
† “Metrodorus says, that about the river Rhyndacus, in Pontus, [serpents] seize and swallow the birds that are flying above them, however high and however rapid their flight” (Pliny, Natural History, book VIII, chapter 14, translated by John Bostock and H. T. Riley).
‡ “And on the banks of the river Rhyndacus while supporting part of their coils on the ground, they raise all the rest of their body and, steadily and silently extending their neck, open their mouth and attract birds by their breath, as it were by a spell. And the birds descend, feathers and all, into their stomach, drawn in by the Serpents’ breathing.” (Aelian, On Animals, book II, chapter 21, translated by A. F. Schofield).
§ “Certain hunters, observing the princely generosity of the king in the matter of the rewards he gave, rounding up a considerable number decided to hazard their lives and to capture one of the huge snakes and bring it alive to Ptolemy at Alexandria. They spied one of the snakes, thirty cubits long, as it loitered near the pools in which the water collects; here it maintained for most of the time its coiled body motionless, but at the appearance of an animal which came dowm to the spot to quench its thirst it would suddenly uncoil itself, seize the animal in its jaws, and so entwine in its coil the body of the creature which had come into view that it could in no wise escape its doom. And so, since the beast was long and slender and sluggish in nature, hoping that they could master it with nooses and ropes, they approached it with confidence the first time, having ready to hand everything which they might need; but as they drew near it they constantly grew more and more terrified as they gazed upon its fiery eye and its tongue darting out in every direction, caught the hideous sound made by the roughness of its scales as it made its way through the trees and brushed against them, and noted the extraordinary size of its teeth, the savage appearance of its mouth, and the astonishing height of its heap of coils. Consequently, after they had driven the colour from their cheeks through fear, with cowardly trembling they cast the nooses about its tail; but the beast, the moment the rope touched its body, whirled about with so mighty a hissing as to frighten them out of their wits, and raising itself into the air above the head of the foremost man it seized him in its mouth and ate his flesh while he still lived, and the second it caught from a distance with a coil as he fled, drew him to itself, and winding itself about him began squeezing his belly with its tightening bond; and as for all the rest, stricken with terror they sought their safety in flight. Nevertheless, the hunters did not give up their attempt to capture the beast, the favour expected of the king and his reward outweighing the dangers which they had come to know full well as the result of their experiment, and by ingenuity and craft they did subdue that which was by force well-nigh invincible, devising a kind of contrivance like the following: They fashioned a circular thing woven of reeds closely set together, in general shape resembling a fishermans creel and in size and capacity capable of holding the bulk of the beast. Then, when they had reconnoitred its hole and observed the time when it went forth to feed and returned again, so soon as it had set out to prey upon the other animals, as was its custom, they stopped the opening of its old hole with large stones and earth, and digging an underground cavity near its lair they set the woven net in it and placed the mouth of the net opposite the opening, so that it was in this way all ready for the beast to enter. Against the return of the animal they had made ready archers and slingers and many horsemen, as well as trumpeters and all the other apparatus needed, and as the beast drew near it raised its neck in air higher than the horsemen. Now the company of men who had assembled for the hunt did not dare to draw near it, being warned by the mishaps which had befallen them on the former occasion, but shooting at it from afar, and with many hands aiming at a single target, and a large one at that, they kept hitting it, and when the horsemen appeared and the multitude of bold fighting-dogs, and then again when the trumpets blared, they got the animal terrified. Consequently, when it retreated to its accustomed lair, they closed in upon it, but only so far as not to arouse it still more. And when it came near the opening which had been stopped up, the whole throng, acting together, raised a mighty din with their arms and thus increased its confusion and fear because of the crowds which put in their appearance and of the trumpets. But the beast could not find the opening and so, terrified at the advance of the hunters, fled for refuge into the mouth of the net which had been prepared near by. And when the woven net began to be filled up as the snake uncoiled itself, some of the hunters anticipated its movements by leaping forward, and before the snake could turn about to face the entrance they closed and fastened with ropes the mouth, which was long and had been shrewdly devised with such swiftness of operation in mind; then they hauled out the woven net and putting rollers under it drew it up into the air. But the beast, enclosed as it was in a straitened place, kept sending forth an unnatural and terrible hissing and tried to pull down with its teeth the reeds which enveloped it, and by twisting itself in every direction created the expectation in the minds of the men who were carrying it that it would leap out of the contrivance which enveloped it. Consequently, in terror, they set the snake down on the ground, and by jabbing it about the tail they diverted the attention of the beast from its work of tearing with its teeth to its sensation of pain in the parts which hurt. When they had brought the snake to Alexandria they presented it to the king, an astonishing sight which those cannot credit who have merely heard the tale. And by depriving the beast of its food they wore down its spirit and little by little tamed it, so that the domestication of it became a thing of wonder. As for Ptolemy, he distributed among the hunters the merited rewards, and kept and fed the snake, which had now been tamed and afforded the greatest and most astonishing sight for the strangers who visited his kingdom. (Agatharchides of Cnidus (2nd century BCE), On the Erythraean Sea, in Diodorus of Sicily (c. 30 BCE), Bibliotheca historica, book III, chapters 36–37, translated by C. H. Oldfather, 1835.)
D2 Two spotted hyenas, labelled ΘΩΑΝΤΕϹ.
This is a unique plural apparently related to the singular θώς which was used indiscriminately for jackals, wolves, and other kinds of wild dogs. The creatures here depicted are spotted hyenas, Sudanese animals, which are also described by Agatharchides†. [Meyboom, pp. 21–22]
† “The animal which the Ethiopians call the crocottas has a nature which is a mixture of that of a dog and that of a wolf, but in ferocity it is more to be feared than either of them, and with respect to its teeth it surpasses all animals; for every bone, no matter how huge in size, it easily crushes, and whatever it has gulped down its stomach digests in an astonishing manner. And among those who recount marvellous lies about this beast there are some who relate that it imitates the speech of men, but for our part they do not win our credence.” (Agatharchides of Cnidus, On the Erythraean Sea, in Diodorus of Sicily, Bibliotheca historica, book III, chapter 35, translated by C. H. Oldfather, 1835.)
E2 A fantastic animal, labelled ΞΙΟΙΓ.
This incomprehensible word is apparently the remnant of a larger inscription. The heavy body of the animal resembles both the rhinoceros [E4] and the hippopotami [B6, B7, D7]. But its striking long snout and sharp teeth are quite different from those of the hippopotami in the lower part, being reminiscent rather of the snout of a crocodile. It looks like a somewhat fantastic kind of hippopotamus. Perhaps it represents the sarkophagus tauros, the ‘carnivorous buffalo’, an Aethiopian animal which is described by Agatharchides†. [Meyboom, p. 22]
† “But of all the animals named, the carnivorous bull is the wildest and altogether the hardest to overcome. For in bulk he is larger than the domestic bulls, in swiftness of foot he is not inferior to a horse, and his mouth opens clear back to the ears. His colour is a fiery red, his eyes are more piercing than those of a lion and shine at night, and his horns enjoy a distinctive property ; for at all other times he moves them like his ears, but when fighting he holds them rigid. The direction of growth of his hair is contrary to that of all other animals. He is, again, a remark- able beast in both boldness and strength, since he attacks the boldest animals and finds his food in devouring the flesh of his victims. He also destroys the flocks of the inhabitants and engages in terrible combats with whole bands of the shepherds and packs of dogs. Rumour has it that their skin cannot be pierced; at any rate, though many men have tried to capture them, no man has ever brought one under subjection. If he has fallen into a pit or been captured by some other ruse he becomes choked with rage, and in no case does he ever exchange his freedom for the care which men would accord to him in domestication.” (Agatharchides of Cnidus, On the Erythraean Sea, in Diodorus of Sicily, Bibliotheca historica, book III, chapter 35, translated by C. H. Oldfather, 1835.)
F2 Two monkeys in a bush, one labelled ϹΦΙΝΓΙΑ,
probably the plural form of the diminutive of sphinx. Here it apparently indicates a sphinx-monkey, one of the species of Aethiopian monkeys given by Agatharchides. It is probably a kind of guenon, like the red monkey. [Meyboom, pp. 22–23]
I think Meyboom means the red-tailed monkey, Cercopithecus ascanius, which is native to South Sudan.
G2 A hyena, labelled ΚΡΟΚΟΤΤΑϹ, “the Aethiopian name for hyena, which is given also by Agatharchides” (p. 23).
H2 A camel-like animal labelled VΑΒΟΥϹ,
which apparently represents a dromedary. The dromedary was not a Sudanese but an Arabian animal. It was not unknown in Egypt but was only introduced on a large scale in the Ptolemaic period. The name nabous is otherwise reported only by Pliny, who states that it was the Aethiopian name for the giraffe. The giraffe and the dromedary were believed to be related animals and so were liable to be confused. [Meyboom, p. 23–24]
I2 An animal with a human head, labelled ΗΟΝΟΚΕΝΤΑΥΡΑ.
Apparently it is a female specimen of the onokentauros, the ass-centaur, a hybrid of man and ass, a variant of the better known centaur. This fantastic animal was described as an Aethiopian animal by a certain Pythagoras who explored the Red Sea coast in the time of Ptolemy II. Perhaps it is based on the gnu, the existence of which seems to have been vaguely known in antiquity. [Meyboom, p. 21]
J2 A guenon.
There are only two major kinds of monkeys in the Sudan, i.e. guenons and baboons. Since this specimen lacks the characteristics of the baboon it must be a guenon. [Meyboom, p. 21]
C3 Meyboom says these are “turtles or tortoises” (p. 23).
D3 Two otters with fish in their mouths. Meyboom says that the barely-visible text above them reads “ΕΝΥΔΡΙϹ, meaning water-animal” (p. 23).
Pliny says, “‘Enhydris’ is the name given by the Greeks to a snake that lives in the water” (Natural History book XXXII chapter 26) but he must have confused the name with that of “snakes of an amphibious nature, known as ‘hydri’ or water-snakes” (book XXIX chapter 22).
E3 Two crabs.
F3 “A guenon probably a green monkey” (p. 23). But this seems doubtful: green monkeys are native to west Africa and not found in Sudan or Ethiopia. Perhaps an olive baboon (Papio anubis), as it resembles the monkey at G3?
F3 Two giraffes, labelled Κ.ΜΕΛΟΠΑΑΛΙ,
originally probably kamelopardalis, spotted camel, the Greek name for the giraffe. The giraffe, which lived in the southern Sudan, was occasionally brought to Egypt as tribute by the Nubians but to the classical world it was first revealed when a specimen appeared in the Grand Procession staged by Ptolemy II. [Meyboom, p. 24]
G3 A monkey labelled ΚΗΙΥΙΕΝ,
probably a misspelling for ΚΗΠΙΟΝ, a diminutive of kepos, a kind of monkey. This creature was first spotted by the explorer Pythagoras and is described by Agatharchides along with the Aethiopian monkeys. The monkey in the Nile Mosaic seems to be a baboon. [Meyboom, p. 25]
G3 A lioness and cub, labelled ΛΕΑΙΝΑ.
H3 A flamingo and an onager. The flamingo is hard to make out in the mosaic, but clear in the dal Pozzo copy:
I3 A carnivore labelled ΔΡΚΟϹ. Meyboom (p. 26) thinks that this is a mistake for ΑΡΚΟϹ, a variant spelling of ΑΡΚΤΟϹ, a bear. Bears are not native to Sudan, but “Syrian bears were occasionally imported into Egypt.”
J3 A pair of cheetahs labelled ΤΙΓΡΙϹ. Meyboom (p. 26) says “Tigris may originally have been a name for the cheetah.”
K3 A large striped snake, perhaps a rock python.
L3 A monkey,
possibly an Anubis baboon [Papio anubis, aka olive baboon]. On the Dal Pozzo copy it is accompanied by the inscription ϹΑΤΤΥΟϹ, probably for satyros, which has not been preserved in the mosaic. [Meyboom, p. 26]
B4 A mongoose fighting a snake, perhaps a cobra.
The deadly rivalry between mongooses and snakes was a popular motif. [Meyboom, p. 27]
E4 A white rhinoceros labelled ΡΙΝΟΚΕΥΩϹ, a mistake for ΡΙΝΟΚΕΡΩϹ.
The African rhinoceros lived in the southern Sudan. Its existence was vaguely known to the Egyptians and became known to the classical world when a specimen appeared in the Procession of Ptolemy II. [Meyboom, p. 26]
F4 A pig-like animal labelled ΧΟΙΡΟΠΙΘΙΚ,
usually completed as choiropithekos, meaning hog-monkey. It probably represents a river-hog, which lived in the southern Sudan. [Meyboom, p. 26]
G4 A lizard labelled ϹΑΥ.ΟϹ ΤΗΧΙϹΝΙΕ,
possibly for ϹΑΥΡΟϹ ΠΗΧΥΑΙΟϹ, meaning a one-cubit-long lizard. [Meyboom, p. 25]
G4 A warthog labelled ΕΦΛΛΟϹ,
which may perhaps be reconstructed as choirelaphos, meaning horned boar. [Meyboom, p. 25]
I4 A spotted cat labelled ΛΥΝΞ.
The African lynx, the caracal, is not spotted. This animal may rather represent a wild cat or perhaps the Sudanese serval. [Meyboom, p. 25]
K4 Two lizards. The upper one is labelled ΚΡΟΚΟΔΙΛΟϹΧΕΡϹΑΙΟϹ “land crocodile. It seems to be a desert monitor” (p. 26) and the lower ΚΡΟΚΟΔΙΛΟΠΑΡΔΑΛΙϹ “which is apparently a Nile monitor” (p. 27).
G6 The question says that the punter has “the head of a Set animal” but Meyboom says:
In the water below the rock a man with a grey beard is punting a papyrus canoe. He wears a loin-cloth, and a lotus leaf as headgear. Apparently he belongs to the poorest class in Egypt. [p. 34]
It’s quite hard to make this out on the mosaic, but maybe it is clearer in the watercolour copy, though I have not been able to find a copy of this section.