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