Racing on twitch with Beyond Chaos

Don't forget, after the 3-switch room, you can choose which party goes down the center path. That party has access to 10 out of 12 shops, one of which is probably the colosseum. So you have an opportunity to direct the best party to the colosseum (ideally they would have a Moogle Charm user too but that's only if you're lucky enough to find one).