When Amenophas reaches a certain percentage, she will lay glowing blue eggs and fly back up to the ceiling. The eggs must be killed immediately or they will spawn harpies.
The first catapult is located to the right as you enter the area ( 539, -2, 392 ) Copy/waypoint 539, -2, 392. Another catapult is across the room at ( 533, -2, 496 ) Copy/waypoint 533, -2, 496.
Packs of gnolls will spawn at the catapults. Kill the gnolls, then fire either catapult. This will update the quest and Amenophas will resume the fight.