There are 15 Trophies that can be collected.

Bronze

A Close Encounter of the Scrolling Kind    
Complete your first Sector.     

Sector Perfecter    
Complete all Sectors in one Stage.     

S Is for SideScroller    
Complete all three Stages.

Mostly Harmful    
Complete any Sector on the Hard difficulty setting.     

Great, kid. Don't get cocky.    
Complete any Sector on the Brutal difficulty setting.     

Triple Crowner    
Get all three hidden Crowns in any Sector.     

You Make Me Wish I Had Three Hands    
Use each weapon one time.     

Spin-a-delic    
Defeat 50 enemies using the Charge Attack.     

You Are the Pris to My Roy     
Complete any Sector by playing with a friend in co-op mode.     

Combolicious    
String together a Combo of 100 points or more.     

Pedal to the Medal    
Receive the highest ranking Medal on any Sector.     

Q-Beams Glitter in the Dark    
Defeat 10 enemies or more using one Laser shot.     

Ender's Game    
Complete any Sector without getting hit by a single shot.

Silver

Spin Long and Prosper    
Complete any Sector without firing a single shot. (Hint: Use the Charge Attack!)

Gold

So Long, and Thanks for All the Bullets    
Defeat the final Boss.

http://www.ps3trophies.org/game/pixeljunk-sidescroller/trophies/