I was able to use the slide kick to unlock this achievement with little trouble. Just group up around 10 or so enemies and just slide back and forth until you hit 1k then slide away.
It does 1 damage so no risk of killing off enemies before your done. You unlock the slide mid way through chapter 2.
One last note after you hit 1000 move away and let the combo end if you are hit you will have to do it again.