The following in-game bug has been reported to DBG:
This quest may or may not still be currently bugged, where if you are a pet-using class, and your pet gets the final killing blow, you will not get credit for killing the Champion. It was believed that a Battlegrounds patch should have fixed this, but some users are reporting that this quest's bug has not yet been resolved. To be safe, back off your pet just before the Champion is dead just to be safe. (This bug also exists with temporary pets, so be careful when you use them in the fight. May 7, 2010: I let my pet get the killing blow today (to check on the bug), and the quest did not update (when this happens, leave the instance and just speak with Shi'jan again to enter).