There are 20 Trophies that can be collected.

Bronze

Hunting companions    
Play a 4 players game in the shooting range.     

Gallic blood    
Hunt a wild boar.     

Proper training    
In silhouette shooting, get an accuracy score of at least 75%.     

Wandering hunter    
Hunt in all available environments.     

Fly away    
Scare off 5 animals in a hunt.

Silver

Man's best friend    
Whistle for the dog 50 times.     

Air shooter     
Hunt 50 ducks.     

Mirror's edge    
Complete a hunting plan 10 seconds before hitting the time limit.     

Sniper    
Hunt a target at a distance of 80 meters.     

Open season    
Complete the Career mode.

Gold

Champion    
Complete the Career mode at the first place.     

Sharpshooter    
Get 100% in a ball-trap game.     

Benefactor    
Kill 100 pests.     

Gunsmith    
Get every weapon in the game.     

Robin Hood    
Hunt 30 preys with a bow     

The Collector    
Hunt an animal of every kind.     

Long chase    
Walk 20 km in Career mode.     

A shadow in the dark    
Get 100% discretion for a hunt.     

Silent hunter    
Hunt a target at less than 5 meters.

Platinum

Hunter's Trophy    
Get all the trophies of Hunter's Trophy

http://www.ps3trophies.org/game/hunters-trophy/trophies/