Here is the full list of all 12 All Zombies Must Die! achievements.
Complete a base quest without taking any damage
Complete ALL character quests
Complete "Return to the Military Base"
Complete "Dev Card Hunt"
Fully upgrade a weapon with any status effect
Kill 500 Zombies in one level
Witness Luxo joining the group
Kill a Mutant with your fists
Witness Brian joining the group
Witness Rachel joining the group
Use your first Smart Bomb
Kill a Zombie