For this one, you need to either have played through the first area to unlock the Zombie map there, or paid real money to unlock them all via the store. To unlock without using money, you'll either need 7 bullets (earned for completing each of the 7 levels - 1 bullet on easy, 2 on medium, 3 on hard) Once you have access to the Zombie map, you need to play through until the first gated area is opened up after the 2nd or 3rd wave. As soon as the animation shows the gate opening, the achievement should pop. Very easy, just kill any zombies you see and keep your distance.
You unlock this through zombie survival mode. The first zombie survival level is unlocked after completing the first seven levels. You could also use command points to unlock it, or even real money, but I strongly suggest against doing so. The first gate will unlock after you complete the first two waves, which, if you have already completed the first seven levels, should be a piece of cake. The achievement will unlock after you complete wave two.