The simplest way to get this achievement, firstly, is to finish scenario campaign mode. By the end, you'll have around 13-1400 kills, if not more.
Once finished with Scenario Mode, pick a character who has a wide range attack you can spam, or just pick a character you're comfortable with. I chose Lars and spammed his upward diagonal RK.
The level you should choose is the Millennium Tower Helipad level. The reason is because there are 90-95 enemies on this level, and they're all killable in one hit, apart from the giant robots(who take around 3-5 depending on your attack boost equipment), making it very suitable for grinding. This place is also suitable to get the "Treasure Master" achievement if you stick a high drop-rate item on one of your characters.
I'm unsure whether kills from your partner go towards this achievement, but after beating scenario mode, and going over Nightmare Train a lot, it only took me eight go-throughs of this level.