Coliseum

The Coliseum, as one might expect, is a combat arena. There is a brief story visit during episode 3 to collect the White Hole Gem Fragment in your quest to defeat the giant flan in the Sunleth Waterscape. You can use this opportunity to pick up the treasure spheres floating around the area that include: 8 Power Bolts, 9 Power Droplets, 7 Power Slivers, 6 Power Chips, and 10 Potent Chips. You'll also want to pick up the Map in an out-of-phase sphere near the entrance. Make a quick run around the area to get 100% completion of the map.

At this time the Arbiter of Time ungraciously kicks you out. It is time to Return to Sunleth Waterscape.

However, through downloadable content you can return to compete against bosses that have the potential to be recruited into your party. Note, however, that their monster crystals are not a 100% drop. You will have to fight these foes repeatedly to get their crystals.