This achievement is made more difficult than necessary due to the game's lack of a block function, but this is best done very early in the game. You should be able to loot a hammer somewhere in the bar/pool area. You can then either wander and wait to find zombies feeding, killing them unaware, or attack the slower zombies with a kick to get them on the ground, then finish them. If you're attacked by multiple zombies when attempting this, don't hesitate to run away. You can get in the grapple sequence while doing this, so long as you don't mess it up. You don't take damage if you're successful. You can also kill using other weapons/methods during your streak, so long as you don't take damage and come back to the hammer at some point.

Another method is to join a friend at the very beginning of a new game with your high level character. The Level 1 zombies will easily die in a single shot.