There are 25 Trophies that can be collected.

Bronze

Getting the Hang of This    
Attain Level 5 with any fighter.

Diversity    
Attain Level 5 with all fighters.

Apply Yourself    
Complete 10 challenges.     

Keep'em Coming    
Complete 20 challenges.     

In the Zone    
Complete 30 challenges     

Relentless    
Complete 40 challenges.

Rookie    
Win 1 ranked match.

Rematch!    
Win 1 Revenge match.

I Let You Win    
Win 1 Final Fight match.

Silver

Multitalented    
Attain Level 10 with all fighters.

Adrenaline Rush    
Complete 50 challenges     

Unstoppable    
Complete 60 challenges     

Rampage    
Complete 70 challenges.     

Domination    
Complete 80 challenges.

Contender    
Win 5 ranked matches.

Run It Back    
Win 5 Revenge matches.

Last Laugh    
Win 5 Final Fight matches.

Gold

Every Fighter has a Story    
Complete all fighter stories.

Master    
Attain Level 15 with any fighter.

Blood. Sweat. Fear.    
Complete 90 challenges.     

Legend    
Complete 100 challenges.

Future Champ    
Win 10 ranked matches.

Double or Nothing    
Win 10 Revenge matches.

Sandbagger    
Win 10 Final Fight matches.

Platinum

Supremacy    
Obtain all Trophies.

http://www.ps3trophies.org/game/supremacy-mma/trophies/