Clear the hall of scarabs without taking damage and using only only cold weapons (sword not included and the player may cycle through weapons but mustn't select unspecified ones).
After getting the second star key you must beat the archers without taking damage and using only cold weapons (sword not included). Make it with a perfect star gem.
Escape from the swarm of gadflies without dying and then beat the mummies with the torch or fists (no damage). Get the third star key with a perfect gem.