There are 28 Trophies that can be collected.

Bronze

Hunt 30 With Bolt     
Hunted 30 animals with the bolt-action rifle in Story Mode     

Hunt 20 With Shotgun    
Hunted 20 animals with the shotgun in Story Mode     

Hunt 20 With Handgun    
Hunted 20 animals with the handgun in Story Mode     

Novice Challenger    
Won five challenges in Shooting Galleries     

Getting The Hang Of It    
Hunted two animals in latching situations in Story Mode     

Focus Novice    
Hunted 10 animals using Focus Shot in Story Mode     

Keep Them Off    
Successfully repelled 10 animals using melee attacks in Story Mode     

A Good Explorer    
Finished the Story Mode on Easy difficulty setting

Silver

The Pro Adventurer    
Finished Story Mode on the Medium difficulty setting     

Hangman    
Hunted 20 targets while hanging in Story Mode     

Focus Master    
Hunted 20 animals using Focus Shot in Story Mode    

Pro Hunter    
Finish three hunts in Story Mode     

Latch Proficient    
Hunted three animals in latching situations in Story Mode     

Survivor    
Hunted 30 animals in a row without dying in Story Mode     

Down Bear, Down!    
Hunted three bears in Story Mode     

Cat Dominator    
Hunted four cougars in Story Mode     

Practiced Challenger    
Won 10 challenges in Shooting Galleries     

Hunt 10 With Semi Auto Rifle    
Hunted 10 animals with the semi auto rifle in Story Mode     

Getting Down    
Landed the plane without hitting any obstacles     

Latch Them Down    
Hunted five animals in latching situations in Shooting Galleries     

The Story’s Taking Shape    
Gathered 15 collectable elements in Story Mode

Gold

The True Adventurer    
Finished Story Mode on the Hard difficulty setting     

Pro Challenger    
Won 15 challenges in Shooting Galleries     

Gold All The Way    
Obtained gold medals in all of the Quick Draw Shooting Galleries     

Latch Master    
Hunted four animals in latching situations in Story Mode     

Shooting Galleries Expert    
Obtained gold medals in all of the Survival Shooting Galleries     

Hunting For Gold    
Obtained gold medals in all of the Trek Shooting Galleries

Platinum

Master of Survival    
Unlocked all Trophies

http://www.ps3trophies.org/game/cabelas-survival-shadows-of-katmai/trophies/