To unlock the Small Tournament trophy in Borderlands: Game of the Year Edition, you will need to complete the small tournament in all three arenas in the Mad Moxxi's Underdome Riot DLC. They are Hell-Burbia, The Angelic Ruins and The Gully.
Enemies in the arenas scale to the host's level, so the easiest way to complete the three arenas is to have the person hosting the game have a low-level character and have some friends with level 50+ characters join.
Each tournament consists of five rounds, which each contain five waves.