The War against the Dunlendings, TA 2758
A Dunlending man Freca, claiming descent from King Fréawine, rode to Meduseld and asked for King Helm's daughter's hand for his son Wulf. Helm, however, mocked him and killed Freca in Meduseld. His people fled for a while. However, four years later they were to return and the battle is detailed below:
Four years later (2758) great troubles came to Rohan, and no help could be sent from Gondor, for three fleets of the Corsairs attacked it and there was war on all its coasts. At the same time Rohan was again invaded from the East, and the Dunlendings seeing their chance came over the Isen and down from Isengard. It was soon known that Wulf was their leader. They were in great force, for they were joined by enemies of Gondor that landed in the mouths of Lefnui and Isen. The Rohirrim were defeated and their land was overrun; and those who were not slain or enslaved fled to the dales of the mountains. Helm was driven back with great loss from the Crossings of Isen and took refuge in the Hornburg and the ravine behind (which was after known as Helm’s Deep). There he was besieged. Wulf took Edoras and sat in Meduseld and called himself king. There Haleth Helm’s son fell, last of all, defending the doors.
Return of the Kings - Book 7, Appendix A: Annals of the Kings and Rulers, II House of Eorl
The end of the war came after the death of Helm, the attack led by Helm's sister-son, Fréaláf, after which he was crowned King and began the Second Line:
‘Soon after the winter broke. Then Fréaláf, son of Hild, Helm’s sister, came down out of Dunharrow, to which many had fled; and with a small company of desperate men he surprised Wulf in Meduseld and slew him, and regained Edoras. ... The Eastern invaders perished or withdrew; and there came help at last from Gondor, by the roads both east and west of the mountains. Before the year (2759) was ended the Dunlendings were driven out, even from Isengard; and then Fréaláf became king.
This is again recounted earlier in the chapter under the Kings of Men:
At the same time the Rohirrim were assailed from the west and the east, and their land was overrun, and they were driven into the dales of the White Mountains. In that year (2758) the Long Winter began with cold and great snows out of the North and the East which lasted for almost five months. Helm of Rohan and both his sons perished in that war; and there was misery and death in Eriador and in Rohan. But in Gondor south of the mountains things were less evil, and before spring came Beregond son of Beren had overcome the invaders. At once he sent aid to Rohan.
ibid: The Stewards
As for the tales of the strength of Helm, these are noted below.
‘Soon afterwards the Long Winter began, and Rohan lay under snow for nearly five months (November to March, 2758–9). Both the Rohirrim and their foes suffered grievously in the cold, and in the dearth that lasted longer. In Helm’s Deep there was a great hunger after Yule; and being in despair, against the king’s counsel, Háma his younger son led men out on a sortie and foray, but they were lost in the snow. Helm grew fierce and gaunt for famine and grief; and the dread of him alone was worth many men in the defence of the Burg. He would go out by himself, clad in white, and stalk like a snow-troll into the camps of his enemies, and slay many men with his hands. It was believed that if he bore no weapon no weapon would bite on him. The Dunlendings said that if he could find no food he ate men. That tale lasted long in Dunland. Helm had a great horn, and soon it was marked that before he sallied forth he would blow a blast upon it that echoed in the Deep; and then so great a fear fell on his enemies that instead of gathering to take him or kill him they fled away down the Coomb.
‘One night men heard the horn blowing, but Helm did not return. In the morning there came a sun-gleam, the first for long days, and they saw a white figure standing still on the Dike, alone, for none of the Dunlendings dared come near. There stood Helm, dead as a stone, but his knees were unbent. Yet men said that the horn was still heard at times in the Deep and the wraith of Helm would walk among the foes of Rohan and kill men with fear.
ibid.: II House of Eorl