This achievement is more of an endurance test than anyhting else so here is a very straightforward solution:
Start the game having already bought the SUV key and completed the mission "meet the contestants" previously. Bash together a couple of Spiked bats and a Defiler (just incase) as you leave the safehouse, grab a couple of Coffee Creamers from the from the Dark Bean then grab the driving book from the BBQ shack in the Americana Casino. From there, get to the red bike on the Platinum Strip and then use it to get to the SUV in the Shamrock Casino. Don't bother aiming for the zombies when you're riding the bike, it's just quicker than walking and you can pick up about 40 kills on the way there. Hop in the SUV and begin your killing campaign and follow the technique below to make sure you get the achievement in the 3-day timeframe.
Like Takun21 said, you can kill around 1,000 zombies in 1 game hour (5 minutes real time) and this is the kind of kill count you want to be aiming for.
Let Katey turn, ignore ALL missions, DON'T leave Fortune Park (this will make sure Leon and the snipers don't appear) and just concentrate on running the zombies over; aim for the bigger groups and reverse over or drive back around to get the ones that were just knocked over by other zombies. Carefully aimed slower driving I found was better than screaming up and down Fortune Park at top speed.
With the driving book in you inventory the SUV will kill 4,000 zombies AT LEAST and will normally explode between 4,300 and 4,500, though this may happen a hundred or so earlier if you bash into things alot.
The quickest way to bag this achievement is to remember how many kills you had when you got in the SUV and save your game every time the SUV explodes.
When your kill count has increased to the next 4,300 or so, make sure that you are near the save point in Fortune Park or down by the red bike at the Arena (so you can ride at speed back to the save point). When it finally goes pop, run over to the nearby save point and save. Then quit, load this save and the SUV will be back where it started, ready to go again. When you've loaded, turn around and take a left towards the hotel, just infront of it you'll find a maintenance cart; use it to drive back to the SUV, aiming at zombies as you go and bagging yourself around 70 kills on the way. Then repeat this technique until glory is yours.
It sounds simple because it really is, but it's also very, very boring. Here are a few extra hints to help you on your way:
* Don't waste time killing scattered zombies if you can help it, the Arena entrance, Bunker entrance and stage always have alot of zombies around. The Park also seems to have alot more nasties at night.
*When driving down to the bunker doors, make sure you go in straight as it's really easy to get stuck downn there. However a successful run down and back can yield more than 80 kills in one go.
*If you leave the park and Leon appears it's not a massve problem. You can kill him (providing you're pretty quick) and still ge the achievement and of course you get the extra bike near the Yucatan incase you get stranded up there. I wouldn't recommend leaving the park for any reason other than getting Leon to appear.
*Don't bother with sliceicles, they don't last anywhere near as long as an SUV & book and waste valuable time to make. Plus you can't pick up the bike book until case 3 or 4.
*Keep your eye on that kill count and make sure you know what number it will be at after the next 4,300. It's very important to be near the save point or the bike when your SUV explodes. This is a tried and tested method.
Hopefully this solution will help, but be warned, the process of getting this achievement is incredibly dull and I would try not to spend any more than 1 hour at a time driving over zombies, simply for your own sanity.
Good luck with this one