The Desert Coliseum can be found to the west of Kasari Lightroot in the Depths.

Coliseum Location
The Desert Coliseum is located to the west of Kasari Lightroot in the Depths.
Coliseum Combatants
Approach the treasure chest in the Desert Coliseum and you will battle a Horriblin, Blue Horriblin, Black Horriblin, a Silver Horriblin then a group of all four types.
Coliseum Reward
The reward for defeating all of the Desert Coliseum enemies is Sheik's Mask.