Manticore attacks mostly with tail, wing and fire breath. Jump on sides or back. Fighting the beast, remember to keep some space behind your backs. When she summons minions, defeat the main enemy first.
After a fight and cut scene, check the room. You find gate blocked by the statues of warriors, eyes of truth locked in the cage in the middle of the room and passage, magically closed by the Fury. Next to it you find four chest. A bit further right you find Archimedes Note.
Open the gate blocked by warriors.
Approach the cage in the middle, look for lever, push it and block with your clone.
Jump into the magic portal before the clone disappears.