After the challenges, you meet Quirrel in a room. He is actually the enemy. To defeat him, get him to destroy the four large pillars in the room. The best way is to stand behind them, wait until he shoots, then move behind the next one. When they are all gone, you both will fall into a room with lots of rocks on the floor and the mirror in the middle. He will walk to the top of the room and shoot at you. Use the mirror as a shield (it bounces his shots back at him). After awhile he will levitate rocks at you. Again, use the mirror as a shield. When he moves to the bottom of the room, keep the mirror between you. Shoot the mirror once with Flipendo and it will swing round and you can use it as a shield again. It will not be long before he is defeated.