There are 11 Trophies that can be collected.

Bronze

BOOM! Hat Shot!    
Shoot off Junction Jack's lucky hat.    

Pistols at dawn    
Finish either 2 player mode    

Six shooter    
Beat your friend in a 2 player game 6-0    

I shot first…    
Defeat any shooter.

Silver

Fastest gun in the west    
Beat Wes Flowers    

Consistently quick    
Get a fastest time of .50 or less for 20 shooters    

There's a new Sheriff in town    
Beat the tournament on Sheriff difficulty    

Quick Draw    
Get a draw time of .30 or less    

Two for one    
Defeat all the shooters who come in pairs

Gold

Fully Decorated    
Earn all of the Badges

1 Secret

Bronze

Premature     
Foul Out

http://www.ps3trophies.org/game/fast-draw-showdown/trophies/