DLC: Zombies: DeceaZed to ExZist Achievement
DLC: Zombies: DeceaZed to ExZist30
Kill 5000 total Gougers, Hot Heads, or Behemoths in any mode.
First and foremost, don't worry about this achievement whatsoever until you have obtained all of the achievements in this add-on. Between running through each movie pitch for the first time and playing through each movie pitch's Score Attack (perhaps several times) for a gold medal, you should make a considerable amount of progress towards this achievement naturally.
Once everything else has been completed and you are finally ready to grind out your zombie kills, load up a Solo session of the fourth pitch, Escape from the Rooftop. As soon as you gain control of your character, drop off the roof and run straight ahead, past the large air duct/unit, and collect some ammo off the table on the right. Now turn around, return to the large air duct/unit, and climb it.
For the next two minutes or so, you're going to stay on this structure and kill all of the incoming zombies as they try to climb up your way. After two minutes have passed, you should automatically progress to the next portion of the level, which spawns you on a rooftop with a high-powered MG overlooking the rooftop below. Mount the MG, aim straight ahead, and open fire on the zombies as they rush you from afar. Soon, you should hear the following dialogue: "So, after the machine gun, the chopper lands." Pause your game at this point, restart the level, and proceed to grind our your kills.
This method should take about four and a half minutes total (including load times) and bump you up 2% (or 100 kills) on your achievement tracker each run. All in all, it's the most efficient way to grind out zombie kills, but it's worth repeating that you should only start worrying about this achievement once all of the other achievements have been obtained.