To get this achievement you will need to play with the Slasher class as it starts with a Stun Gun. It is recommended to do this offline to prevent other players from killing the zombies you want to target (Or try to do this with a session only with friends if possible).
Finally, after choosing the Slasher just give a single shot that reaches 10 zombies (To shoot with the Stun Gun you must press the LB button). I got mine in NY in Chapter 1 shortly before reaching the train driver (there is a small horde attacking the main train wagon before you talk to the train driver). My friend got his in NY in Chapter 1 also but he got when the zombies begin to climb the first big wall while we are still in the Mall (shortly after descending the escalators). In some attempts you should get it.