There are 36 Trophies that can be collected.

Bronze

Up And Comer    
First challenge complete!    

Midway Tour    
Play each of the seven basic Carnival games.    

Magic Mirror    
Magic Mirror completely unlocked!    

Restoration    
First Carnival building fully restored!    

Seaside Set    
Wake up the Goldfish, the Jellyfish and the Lake Monster.    

Funky Trunks    
Wake up the Baby Mammoth and the Elephant.    

Bird Watcher    
Wake up all Bird Pets.    

Extinction Distinction    
Wake up all Extinct and Mythological Pets.    

Any Way    
Play one Party Time multiplayer game.    

My Way    
Play one Pick and Play multiplayer game.

Silver

Every Way    
Play one of every multiplayer game.    

Pass It    
Play 10 pass-the-motion controller multiplayer games.    

Side-By-Side    
Play 10 Side-by-Side multiplayer games.    

Boardwalk Reopened!    
All buildings reopened in Boardwalk!    

Shell Beach Reopened!    
All buildings reopened in Shell Beach!    

Ferris Park Reopened!    
All buildings reopened in Ferris Park!    

Tree House Way Reopened!    
All buildings reopened in Tree House Way!    

Gossip Hound    
Listen to all the gossip Granny and the Carnies know.    

Chotchkies!    
All souvenirs won!    

Animal Friend    
All pets woken up!

Platinum

Carnival Master    
All Trophies Won!

15 Secret

http://www.ps3trophies.org/game/carnival-island/trophies/