Balasiel can be tricky to find. Start by going to Watchdog Alley at (F-6). You will see an NPC named Celyddon, walk west from him into the stairwell. Follow it upward, and take your first left (do not walk out along the wooden walkway, walk across the wooden bridge instead). Follow those stairs up, then they will dip back down, and curve around to Balasiel.
Obtain a Revival Tree Root (available in the Auction House under Materials -> Alchemy) and trade it to Balasiel to complete the quest.