Note: This must be done in Sandbox mode and only the host's kills will count.
Start going for this once you have all single player & co-op challenges done, as this will mean less kills for you to grind. To do this method you will need the SUV.
To get the SUV, grab the two gambling mags. The first is on the second floor of the BBQ Shack in the Americana Casino and the second is on the second floor of the Grotto in the Palisades. Once you have them go to the Slot Ranch Casino and bet on the large slot machine next to the large corridor leading to the food court. Now just sit here betting until you hit $2,500,000. Once you have that much, go to the pawn shop on the Silver Strip and buy the SUV key.
You will then want to go get the driving magazine too so that makes the SUV last 3 times longer. It is located on the roof of Paradise Platinum Screens on the Platinum Strip. You have to climb the snack machine right next to Cash Gordan's Casino and climb up, then you follow the walkway all the way round. You will then need to jump to the roof of Jugz Bar & Grill, then jump to the roof of Paradise Platinum Screens.
Once you have the magazine go and get the SUV. Then drive the SUV up and down the strip running over zombies. As soon as the SUV begins to smoke it's a good idea to go into the underground then come back, so another spawns. Simply then use the SUV until it breaks and get the new one when it does. Rinse and repeat. This will take you a while and will be a grind. It'll also most likely be the last achievement you get.
Click here for more help on getting the achievement.