There are 31 Trophies that can be collected.

Bronze

Spoorer    
Find 20 tracks in Story.

Detective    
Spend 15 minutes total in detection mode.

Bushman    
Spend one continuous minute fully covered by vegetation.

Anatomy Saved My Life    
Win 10 skillshots in Story.

Paparazzi    
Take 30 pictures in Story.

Archer    
Hunt a bird using the Compound Bow.

Good Reflexes!    
Hunt 10 Target of Opportunity animals.    

Hunting The Hunters    
Shoot 10 predators during a single player Arcade Shooting Gallery.

Demolition Expert    
Shoot 10 exploding cans in single player Target Shooting Galleries.    

True Hero    
In any 1 Player Arcade Shooting Gallery make your Hunter Award reach five stars.

Silver

Pump It Up    
Hunt 300 birds with the Shotgun in Story

Hungry for Fame    
Upload 20 pictures.

Gun Slinger    
Shoot 10 trophy animals while using the Trophy Gun.

Shadow    
Finish any location in Story without alerting any trophy animal.

Heartbreaker    
Hunt 10 big game trophies by shooting them through the heart.    

Secret Seeker    
Find 7 hidden locations in Story.

Close and Personal    
Shoot any big game from less than 15 yards.    

Devarminator    
Hunt 200 small game land animals in Story.

Skill Or Luck?    
Hunt any trophy with one shot over 280 yards.    

Bow Master    
Hunt 15 big game trophies while using the Compound Bow.

Lucky Luke    
Hunt an animal from at least 40 yards without using your scope or sights.    

Adrenaline Seeker    
a trophy animal while it's alerted and running away.

King of Reflexes    
Win any 1 Player Reflex Shooting Gallery hunting all animals in the correct order.    

Deadeye    
Win any single player Shooting Gallery while not missing a shot and scoring 20000 or more.

Let Them Fall    
100 birds in single player Shooting Galleries.    

Clean!    
Hunt at least 75% of male animals in any single player Arcade Shooting Gallery.

Gold

Pimp My Gun    
Unlock and fully upgrade all the firearms.

Hunting for Money    
Earn more than $50,000 in Story

Gun Master    
Finish every Story map using only the Trophy Gun and the Compound Bow.

Become a Legend    
Finish Story Mode.

Platinum

Platinum trophy    
Unlock all other trophies.

http://www.ps3trophies.org/game/cabelas-big-game-hunter-2012/trophies/