There are 50 Trophies that can be collected.

Bronze

Tale of Naruto Uzumaki complete     
Completed Tale of Naruto Uzumaki.     

Tale of Sasuke Uchiha complete    
Completed Tale of Sasuke Uchiha.     

Tale of Young Naruto complete    
Completed Tale of Young Naruto.     

Substitution Jutsu Master    
Substitution Jutsu collected: 80%     

Ninja Info Card Collector    
Ninja Info Card images collected: 50%     

Ninja Tool Master    
Ninja Tools collected: 80%     

Image Master    
Images collected: 80%     

Ultimate Jutsu Movie Master    
Ultimate Jutsu scenes collected: 80%     

First S Rank!    
You've earned your first S Rank in a battle.     

Introductory Stage Survivor!    
You've completed all of Introductory Survival.     

Beginner Survivor!    
You've completed all of Beginner Survival.     

Intermediate Survivor!    
You've completed all of Intermediate Survival.     

Advanced Survivor!    
You've completed all of Advanced Survival.

Team Seven Tournament Champ!    
You've completed the Team Seven Tournament.     

Sand Genin Tournament Champ!    
You've completed the Sand Genin Tournament.     

Leaf Genin Tournament Champ!    
You've completed all Leaf Genin Tournament battles.     

Boy's Life Tournament Champ!    
You've completed the Boy's Life Tournament.     

New Team Seven Tournament Champ!    
You've completed the New Team Seven Tournament.     

Leaf Chunin Tournament Champ!    
You've completed the Leaf Chunin Tournament.     

Ultimate Ninja Tournament Champ!    
You've completed the Ultimate Ninja Tournament.     

Leaf Higher-Up Tournament Champ!    
You've completed the Leaf Higher-Up Tournament.     

Shippuden Tournament Champ!    
You've completed the Shippuden Tournament.     

Peerless Ninja Tournament Champ!    
You've completed the Peerless Ninja Tournament.     

Akatsuki Tournament Champ!    
You've completed the Akatsuki Tournament.     

Five Kage Tournament Champ!    
You've completed the Five Kage Tournament.    

First Shopping!    
You've done your first shopping.     

First Ninja Tool Edit!    
You've edited a ninja tool set for the first time.

Silver

10 Down    
You've defeated 10 opponents in Ultimate Survival.

Wealthy Ninja    
You've earned a total of 1,000,000 Ryo.

Platinum

I'm the greatest ninja!    
You've acquired all trophies.

20 Secret

http://www.ps3trophies.org/game/naruto-shippuden-ultimate-ninja-storm-generations/trophies/