There are 21 Trophies that can be collected.

Bronze

Discoverer    
Find hidden stuff!     

Staying Alive    
Stay alive     

MacLeod    
Don't die!     

Apprentice    
Kill a lot of Gobos!     

Hitman    
Kill a bunch of Gobos!     

Second Blood    
Kill loads of Gobos!     

To the Max    
Play for some time!     

Maxed Out    
Play a lot!     

Sticking Around    
Spend a long time on a single level!     

Getting STARted    
Score three stars in a lot of levels!     

Star Spangled Max    
Score three stars in a load of levels!     

AllStar    
Score three stars in all levels!     

Cannibal Soup    
Boil to death!     

Epic Battle    
Take your time beating Mustacho!     

Ninja Vanish    
Kill Mustacho! Fast!     

Mexican Mouse    
Beat a few time records!     

Speedster    
Beat a stack of time records!     

Schumi    
Beat all time records!     

Ship Ahoy    
Unlock the Pirate World!     

We are the Robots    
Unlock the Robot World!     

Victory    
Beat the game!

http://www.ps3trophies.org/game/max-and-the-magic-marker-gold-edition/trophies/