Skeldritch will shoot boulders at you. Use the sand wand to stop a boulder before it can roll off of the arena. Boulders can shoot through a thin layer of sand, so try to make it at least two squares thick to catch the boulder. Then, use the sand wand to push the boulder onto a catapult. Get any other boulders out of the way of the catapult, then hit the purple orb next to the catapult to shoot the boulder at Skeldritch. This will make it lose one of its segments, becoming shorter.
After that, Skeldritch will shoot out three boulders at a time, so be careful not to let them smash each other apart. Also, Skeldritch will shoot a red laser at you, so be sure to run out of the way when that happens.
Continue putting boulders onto catapults. Some of Skeldritch's segments are armored, so you need to make sure to only hit the part of the segment that is not covered with armor. Skeldritch will always turn to face you, so run to a place in the arena that will make Skeldritch turn his vulnerable spot toward the catapult with a boulder in it. Then use the boomerang or bow and arrow to activate the switch.
Watch out for when Skeldritch shoots out high-speed red boulders. You need to use thicker sand to stop these.
After destroying all of the segments, Skeldritch's skull will bounce around the field. Trap it with sand, and then have Link get up on a sand pillar behind Skeldritch so he can hit the purple gem with his sword. Do this until you have defeated Skeldritch.
Afterward, go downstairs to get the Bow of Light. Shoot the eye behind the treasure chest with a light arrow by holding the stylus on the touch screen until the light arrows charge up, then release the stylus to shoot the light arrow. Go into the blue spot to return to the entrance.
You will learn that you need to go back to the top of the Tower of Spirits and find the altar to get the Compass of Light, which will lead you to the Demon Train.