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