Dead Rising 2

Original solution on 360 by "diesel680"

Note: The "special" zombies will only come out when playing through the main story, so you have to be on track to earn Ending A or Ending S by getting to at least 6-1 on the case files in order to earn this achievement.

You should have plenty of time to get this achievement after finishing case 7-3 but before completing The Facts. You should also have time during Overtime mode.

NOTE: Make sure that you beat Leon in the case Meet the Contestants so that you have a motorcycle garage where you can modify the motorcycles.
The motorcycle garage is right by the entrance to the Yucatan. There is a chainsaw by the maintenance room by Hot Excitorama on the Silver Strip (use the in-game map to find store names and locations). Take the chainsaw to the motorcycle garage and combine them to make the slice cycle.

You can then use the newly opened entrance to the maintenance tunnels in the top right corner of the silver strip, across from the motorcycle garage to get down there, where there are a large of amount of special zombies. Not all zombies were affected by the gas, so you will probably have to kill more than 1,000 zombies in order to kill 1,000 special zombies.

The slicecycle will break down after 1,000 zombie kills, so head back up to the Silver Strip once you have killed around 900 zombies. That way you won't be stuck down in the maintenance tunnels with the special, and thus dangerous zombies.

Make a new slicecycle and repeat until the achievement pops. Be sure to have a large supply of healing items in case you get into trouble and some melee weapons to protect yourself if your motorcycle breaks. The special zombies can still hurt you on your motorcycle with their vomit attacks, so watch your health.

This has to be done in one playthrough, but this method is safe and effective, and you can easily earn the Wrong kind of "Chopper" achievement at the same time.

You should finish with plenty of time to finish "The Facts", but if you don't, keep an old save and reload it. There's no reward attached to the achievement.

NOTES:

the Bikes magazine will give your Slicecycle 3X Durability.That means it will last for 3000 kills, and saving you the effort of making more slicecycles,. It is located in the Slot Ranch Casino, side room off of the northern most security room.