Here is the full list of all 12 OMG Zombies! achievements.
Prestige the Game once
Complete the game to 100% (all Platinum medals)
Get all upgrades in all categories
Shoot a Cop Zombie and have their bullet kill five other Zombies
Finish the game getting the best ending
Get all Upgrades in a single category
Complete a level by only shooting Barrels
Get a Platinum medal with a single bullet
Kill 5 other Zombies by shooting a Taser Zombie
Get a Platinum medal
Finish the game with any ending
Prestige 20 times