The subject of this article originates from non-canonical sources. To find out about what is considered "canon" see LOTR:Canon.
During his assault to Amon Sûl the Witch-King sent troops to attack Rivendell as a diversion so the elves would not attack his forces at Amon Sûl. The elves were outraged by this attack and started to understand the threat Angmar was so they helped King Araphor of Arthedain to defeat Angmar in Arthedain and soon the Witch King had retreated to Carn Dûm. Elrond summoned the elves of Lindon, Rivendell and Lórien to march against Angmar to destroy it forever.
Rogash and Morgomir awaited with reinforcements in a camp West of the city so a beacon was lit when the elves arrived. The elves started to attack the main gate but the Witch King and a small contingent defeated those using secret postern gates. The elves then tried to attack the eastern walls which were far from the Witch King and his troops yet some orcs of Gundabad where hidden in the trees and destroyed the catapults. Then an earthquake summoned by the elves destroyed a section of the eastern wall and allowed the elves to get into the city. The Witch King mustered his troops against the elves yet as more waves of elves arrived the Witch King was forced to flee to the second level. Hwaldar managed to gather the men of Rhudaur and they stood against the elves allowing the Witch King and the main army to reach the second level. Hwaldar and his men were all slain. The Witch King managed to maintain the second gate for some time killing many elves yet the gate was lost after a short time. The armies of Angmar clashed with those of the elves and the elves seemed to be defeated for a while until Glorfindel and Elrond arrived with the main army. The Witch King knew he could not face that huge army with the few men that remained so he fled directly to the citadel. The catapults of the elves kept shooting flaming projectiles against the walls and the gates yet the cold sorcery of the Witch-King managed to save the walls from major harm.
Suddenly Morgomir and Rogash arrived with a great army of trolls and evil men, amongst these some terrible sorcerers. The gates of the citadel opened and the two armies of Angmar surrounded the elves. The battle turned into carnage and only few elves survived including Elrond and Glorfindel. Angmar managed to win the day yet it was left in such a bad state that even Arnor could finish what the elves started, so the Witch King had a plan to recuperate while Arnor would have no chance to recover.
This battle was not in the books and was invented solely for the video game The Lord of the Rings: The Battle for Middle-earth II: The Rise of the Witch-king.