Olympus Coliseum

The Olympus Coliseum is the second (or 3rd or 4th depending on what order you go)world of Kingdom Hearts. It is the site of several battle tournaments.

Getting started
When first arriving at the coliseum, you will meet Phil. He'll sign you up for the preliminary trails--which you would have to pass in order to enter regular tournaments.

The Battle with Cloud
Before you actually could participate in the tournaments, you must first defeat Cloud and Cerebrus as part of the story. Phil would then allow you to participate in the exams.

Tournaments

 * 1) Phil Cup
 * 2) Pegasus Cup
 * 3) Hercules Cup
 * 4) Hades Cup
 * 5) Gold Match
 * 6) Platinum Match

Kingdom Hearts Birth By Sleep
In a screenshot of Kingdom Hearts: Birth by Sleep, Terra, Ven, and Master Xehanort are all seen in Olympus Coliseum.