There are 19 Trophies that can be collected.

Bronze

n00B SAuCe    
Complete your first level in Arcade mode.    

Super Combo    
Achieve a combo over 6.    

Ascended Unity    
Complete Co-Op Arcade mode.    

True Master    
Get every feat in a single level.    

The Whopper    
Score over 1,000,000 points from a single line.     

Mosaic     
Complete a level by cutting away 250 lines or more.     

Top Gun    
Kill 101 or more enemies in a single level.     

Betrayal!    
Kill 2 or more friends in Co-Op.    

88 Miles-An-Hour    
Complete a level in less than 8.88 seconds.    

Mr. Popular    
Complete a 7-player Deathmatch game.    

Light Speed    
Beat level 36 in under 40 seconds. (Single player Arcade mode only.)    

Fully Bronzed    
Complete all Challenge levels to at least Bronze standard.    

Risky Business    
Pick up 500 negative (red) Powers.

Mammoth Score    
Score 5,000,000 points or more on a single level.

Do Robots have feelings?    
Complete Arcade Mode.

Silver

G.O.A.T    
Complete all Challenge levels to Platinum standard.

Mad Skillz    
Complete Arcade mode in a single run.

2 Secret

http://www.ps3trophies.org/game/cubixx-hd/trophies/