Best done on Sandbox mode since you have access to the Bike in the trailer early on.
Grab a chainsaw from the top of the stage (climbing up the speakers on the left) and run it back to the Bike. Customize it with the chainsaw and you'll have a chainsaw upgrade on the bike.
Simply drive around the Strip mowing down as many zombies as you can.
It shouldn't take you more then 1 or two bikes to get 1337 zombies.
When you have the achievement, you'll also unlock the Ninja Torso/Pants.