In Story Ocean, when you engage in battle, there are several prizes you recieve from accomplishing a certain goal when you defeat enemies in a certain amount of time or defeat a certain enemy. Here are some the unlockables you recieve when you reach a certain point, well collect enought Battle Trophies.

Battle Collection Unlockables
Unlockable	How To Unlock
2P Costumes	Complete 15% (045/300) of the Battle Collection
3P Costumes	Complete 40% (120/300) of the Battle Collection
4P Costumes	Complete 80% (240/300) of the Battle Collection
Fourth Dimension Mode	Complete 65% (195/300) of the Battle Collection
Full Active Mode	Complete 95% (285/300) of the Battle Collection
Music Test	Complete 55% (165/300) of the Battle Collection
Universe Mode	Complete 25% (75/300) of the Battle Collection