There are 12 Trophies that can be collected.

Bronze

Space Explorer    
Complete the game with any Lion.

Defender of the Universe    
Rescue 100 groups of civilians.     

Lion Heart    
Complete any level without the Lion deactivating once.

Zarkon's Bane    
Complete any three levels without seeing a game over in a single play session.     

Fly Swatter    
Achieve ten air pounces in a single level.     

The Vendetta Begins    
Beat a friend's level score after they have beaten yours in the same online game session.

Lion Ace    
Earn a x10 score combo five times in a single level.

Silver

King Alfor's Blessing    
Get five Survivor bonuses in a single play session.

Five Keys    
Complete a level in an online game with four other players.

Carried the Team    
Complete a level in an online game where you are the only surviving player.

Blazing Victory    
Kill a Robeast without Voltron losing any health.

Gold

Space Legend    
Complete the game with all five Lions.

http://www.ps3trophies.org/game/voltron-defender-of-the-universe/trophies/