There are 12 Trophies that can be collected.

Bronze

The Bitter End    
Complete the challenge 'The Bitter End'.    

Big Finish    
Complete the first tier of the challenge 'Big Finish' in any mode.    

Sharing Is Caring    
Complete the challenge 'Sharing Is Caring'.    

Couch Potato    
Complete the first tier of the challenge 'Couch Potato'.    

EX-ceptional    
Complete the third tier of the challenge 'EX-ceptional' in any mode.    

Wax On, Wax Off    
Complete the third tier of the challenge 'Wax On, Wax Off' in any mode.    

Super Artist    
Complete the third tier of the challenge 'Super Artist' in any mode.

Silver

Going Streaking    
Complete the second tier of the challenge 'Going Streaking' in ranked online mode.  

Practice Makes Perfect    
Complete the challenge 'Practice Makes Perfect'.    

Sticks & Stones    
Complete the first tier of the challenge 'Sticks & Stones' in any mode.

Mystery Man    
Complete the challenge 'Mystery Man'.

Gold

Pocket Full Of Quarters    
Complete the challenge 'Pocket Full Of Quarters'.

http://www.ps3trophies.org/game/street-fighter-iii-3rd-strike-online-edition/trophies/