At the Battle of Tara in 980 C.E. the Norse were (apparently) heavily defeated by the Irish. There is not much material or sources on this battle. Does anyone have ideas on how the Irish were able to win?
No one knows.
The battle of Tara led to the siege of Dublin and further defeat for the Vikings.
The Annals of the four masters has this to say:
The battle of Teamhair was gained by Maelseachlainn, son of Domhnall, over the foreigners of Ath-cliath and of the Islands, and over the sons of Amhlaeibh in particular, where many were slain, together with Raghnall, son of Amhlaeibh, heir to the sovereignty of the foreigners; Conamhail, son of Gilla-Arri; and the orator of Ath-cliath; and a dreadful slaughter of the foreigners along with them. There fell also in the heat of the battle Braen, son of Murchadh, royal heir of Leinster; Conghalach, son of Flann, lord of Gaileanga, and his son, i.e. Maelan; Fiachna and Cuduilich, the two sons of Dubhlaech, two lords of Feara Tulach; and Lachtnan, lord of Mughdhorn-Maighen. After this Amhlaeibh went across the sea, and died at I-Coluim-Cille.
A great army was led by Maelseachlainn, son of Domhnall, King of Ireland, and by Eochaidh, son of Ardgar, King of Ulidia, against the foreigners of Ath-cliath; and they laid siege to them for three days and three nights, and carried thence the hostages of Ireland, and among the rest Domhnall Claen, King of Leinster, and all the hostages of the Ui-Neill. Two thousand was the number of the hostages, besides jewels and goods, and the freedom of the Ui- Neill, from the Sinainn to the sea, from tribute and exaction. It was then Maelseachlainn himself issued the famous proclamation, in which he said:— "Every one of the Gaeidhil who is in the territory of the foreigners, in servitude and bondage, let him go to his own territory in peace and happiness." This captivity was the Babylonian captivity of Ireland, until they were released by Maelseachlainn; it was indeed next to the captivity of hell.
It may be that this account represents almost everything that remains known about the event.
So whether it was overwhelming numbers, a better defensive position, better tactics, better supplies or some other factor or combination of factors is probably unknowable.
According to Wikipedia: "the Hill of Tara, according to tradition, was the seat of the High King of Ireland." so, if occupied by the forces of Mael Sechnaill and allies, it's cultural significance to them ought to have been a factor affecting their morale. The defensive earthworks at the top a hill may also have been a helpful factor in a three-day battle.
I don't know if there are other accounts in Irish sagas or elsewhere that provide a lengthier or more detailed description, if so we have to take into account that such stories tend to flatter their sponsors.