When you first enter the room you will be greeted by several spectral enemies.
For the puzzle, the first crystal to your right when you enter the room must be hit with an Aard. The one beyond that on the right must be hit with an Igni. The first one on your left must also be hit with an Igni. The one beyond that on the left must be hit with an Aard. Whether there is a time limit or not is unknown. There doesn't seem to be a "correct" order, however.
When you complete the puzzle, a door in the room will open. Going through that door, and then another door, you will fine a statue with a sword at the base of it. Upon taking the sword, a mage guard will appear and attack you. When he goes up on the ledge, he will summon wraiths to attack you, while attacking from afar.
Upon defeating the guard, another door will open. Here a wraith and 2 or 3 bruxas will attack you. After this, there only remains looting this last room.