Proving once again that anything is possible with creative use of game mechanics,Shantál on Al'akir (EU) has successfully soloed the heroic version of the Alysrazor encounter. I've done some soloing myself in the past, and I can say that this is one of the most impressive individual feats I've seen, especially from a non-tank class. To my knowledge, this is the first heroic tier 12 encounter to be soloed, period.
According to Shantál, many hours were spent "figuring out the tactics, pushing DPS to the limit, and not going crazy after dozens of near kills." For a full strategy explanation, check out the thread on MMO-Champion.