There are 13 Trophies that can be collected.

Bronze

Master of Shibuya    
Complete "The Return of the Tosas."    

Underdog    
Complete "Shattered Pride."     

Jungle Boy    
Survive 30 years in SURVIVAL.    

Pedigree    
Survive for 10 generations in SURVIVAL.    

Furry Fashionista    
Wear a complete series of clothing.    

Jungle Baby    
Complete the tutorial.    

World Debut    
Enter the online rankings.    

First Mate    
Mate with a female in SURVIVAL.  

First Hunt    
Defeat an animal in SURVIVAL.

Silver

Tokyo Jungle    
Complete STORY and view the true ending.    

Jungle Man    
Survive 45 years in SURVIVAL.    

Can-Do Creature    
Finish all challenges in single playthrough.

Gold

King of the Jungle    
Survive 100 years in SURVIVAL.

http://www.ps3trophies.org/game/tokyo-jungle/trophies/