While playing through the game, use your jump kick move ( then ) to kill zombies. While leveling up, you'll receive additional barehanded moves. Not only are these moves fun to mess around with, they'll make killing zombies quite a bit easier. There is a magazine located in "Ragazines" inside the Royal Flush Casino. The magazine is called; Hand-to-Hand. Use this to help you with your kills.
The kill count is spread across all playthroughs, given you restart the story from a previous save, but there have been reports of it not unlocking, so it's best to contain them in one playthrough, just to be on the safe side.
Note: The moves you receive while leveling are random. Don't worry if a certain skill hasn't unlocked yet, you'll get them all eventually.