I recommend a high level for this achievement, as you will need more skill moves and especially attack power, although all you really need is the double lariat.
It would sound easier to get this in the maintenance tunnels, but a lot of food would be needed, so don't go there.
I did this in Paradise Plaza; stocking up on OJ at Columbian Roastmasters.
When you do a double lariat, make sure you have your hands free (press up on the D-Pad), otherwise you'll be throwing food all over the place.
If you throw a zombie into other zombies, the thrown zombie will be counted as a weapon; not a barehanded kill, so if you do this you will need to kill some more after 1,000.