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