To clearly delimit dates and places, I ask for information about the rulers before 1000 BC in the Fertile Crescent or Eastern Mediterranean. Historians may be Greek, Roman, or peoples belonging to the Hellenistic world, such as Egyptians (Maneto), Chaldeans (Berosus) or Jews (Josephus).
I am thinking of leaders like Sargon of Akkad, Hammurabbi, Tuthmoses III or Ramses II. They were extremely famous in their time and comparatively almost as powerful as the Great Kings of Achaemenid Persia only a few centuries later, but I dont find texts from the classic antiquity that speak of them.
The Bible alludes to the city of Pi-Ramesses, but the other pharaohs that it names are much more modern: Taharka, Nechao, Shoshenk, all belong to the last years of an independent Egyptian kingdom, about 600 BC. The Bible also contains no clear allusions to rulers of other empires prior to David and Solomon. There is a "Nimrod" in the Genesis who may be an Assyrian king called Ninurta from 1200 BC but may also be an Assyrian god with the same name.
Maneto, an Egyptian priest, is quite accurate in his list of pharaohs and quotes several Ramesses but the Egyptian priests who talked to Herodotus seem to remember that a Pharaoh called Sesostris (Senusret III) was far more powerful than Ramses II or Tuthmosis III, something that is not true.
I have not been able to find useful information in Berossus, which seems the most mythological of all.