Here is the full list of all 12 All Zombies Must Die! trophies - there are 7 bronze, 4 silver and 1 gold.
Complete ‘Dev Card Hunt!’
Kill a mutant with your fists
Complete all character quests
Complete ‘Return to the Military Base’
Fully upgrade a weapon with any status effect
Witness Luxo joining the group
Witness Brain joining the group
Witness Rachel joining the group
Kill 500 zombies in one level
Use your first Smart Bomb
Kill a zombie
Complete a Base quest without taking any damage