Ojo, I had the same issue tonight when doing this quest with a friend. Personally, I found the boss monotonous, tedious and boring. 20 minutes to kill this guy. Only to have killed him, but the quest doesn’t trigger.
I filed a bug report in game with an attached screenshot. I hope they rectify this because right now all I want to do is complete the story quest and I can’t. And, there is NO way I’m going through that 20 minute fight again if there is a chance the quest is still bugged.