There are 12 Trophies that can be collected.

Bronze

Jack the Builder    
Put blockades on every door and window in one level.

Nightshift    
Play five minutes in darkness.

Bomber    
Kill twenty zombies with a single bomb trap.    

Work force    
Employ 20 construction zombies at the same time.    

Dead can Dance    
Activate the Jukebox and make a zombie dance.    

Cactustime    
While playing Mike, search four cacti in a row.    

Quintupel Super Awesome    
Build five blockades with super awesome finish in a row.    

Multikill    
While playing Foxy, kill three zombies with one melee attack.

Silver

Poo Dance    
Make ten infected zombies dance at the same time.

All Traps    
Build every trap and a wood blockade in one level.

Game Complete    
Complete all singleplayer levels.

Gold

Medal Seeker    
Win all gold medals in all singleplayer levels.

http://www.ps3trophies.org/game/dead-block/trophies/