I'm assuming that you've already gotten every other achievement already, if not, I suggest you do, since that will knock out a good chunk of the kills needed for the achievement.
I also highly recommend you have 20 manuscript pages, so that you can use the assault rifle.

To start off, Load up Act 2 Part 3 (go to 'Story Mode' and 'Replay Scene', Choose 'Normal' then 'Act II: Relapse').
You'll start at the entrance to the Drive-In. Grab the Generator Building Key and then run down past the viewing lot. Grab the assault rifle before going into the Generator Building.

Now, go into the building and make sure you refill your ammo before turning on the power.
This will be your checkpoint that you reset to.

Now time for the kills.
After you turn the power on, spiders will start spawning in to attack you. these little guys are going to be what we're killing. Yes, they DO count towards the achievement.
Inside the building a total of 12 will spawn, you'll want to make you're way outside of the building killing some spiders along the way. Make sure not to get shocked or to make any Cinematic Dodges, as these will just slow you down a bit.


Once you're far enough outside, another 10 will start spawning in and the ones from inside will continue following you. Kill all of the spiders from here and then hit 'ESC' and 'Restart Checkpoint'.
Rinse and Repeat.

Once you get the hang of it, each run will be right around 1 minute long. Assuming you have around 1,000 kills from getting the rest of the achievements, this should take less then an hour to net you the achievement.

Tips
- I recommend shooting the barrel as you leave the building to give yourself better line of sight for the spiders.

- If you have decent enough aim, you can fire just one bullet at each spider and not have to spend time reloading

- If you count your kills each run, then you can quickly reset after you count to 22 rather then waiting to see if you missed any kills