Here is the full list of all 12 ZED Patrol achievements.
As a team kill 1000 Zeds in a single run
Complete a run without shooting any bullets
Equip every type of gun in a single run
As a team get 10 revives in a single run
Complete the tutorial
Complete a run in under 15 minutes
Get 25 headshots in one run
As a team blow up 100 cars in one run
Lose a run
Complete a run without anybody on your team dying
Complete a run after having shot at least 1000 rounds
Kill at least 10 zombies with one grenade