There are 12 Trophies that can be collected.

Bronze

You Win    
Win a match in Arcade Mode without losing a round (any difficulty level)    

Ring Out    
Win a round by knocking your opponent out of the ring in Arcade Mode (any difficulty level)    

Excellent    
Win a round without taking any damage in Arcade Mode (any difficulty level)

Score Attacker    
Play Score Attack Mode

Up and Coming    
Play one ranked match    

Challenger    
Play ten ranked matches    

Student    
Play any training session in Tutorial Mode

Silver

VS Dural    
Face off against Dural in Arcade Mode (any difficulty level)

5 Hit Combo    
Perform a five-hit combo in Score Attack Mode    

Test Complete    
Complete a test in License Challenge Mode    

Five Tests Complete    
Complete five tests in License Challenge Mode

Gold

Ten Tests Complete    
Complete ten tests in License Challenge Mode

http://www.ps3trophies.org/game/virtua-fighter-5-final-showdown/trophies/