In order to get the key to unlock the cage, need to jump on moving platforms. Avoid the black ones. Wait until they turn white. Make sure that you kill the people in the towers, as they will shoot arrows at you. You also need to check on the
wizard because he will be taunted by black knights. After you get to certain points on the platforms, they will begin to change course. After you get the arrow, shoot the doors and you and the wizard will be free.