Prodeus

While this achievement may seem like a slog at first, it's worth noting that you can work towards this a lot easier with custom maps in the workshop.

I've created two such levels with over 4500 zombies each where all you need to do is enter the level on the 'Ultra Easy' difficulty, run around through the ammo/health in front of you, and blast away with the Chaos Caster you spawn with, making sure to fully charge all your shots with the secondary fire button (default is ) for more damage & to use less of the finite ammo refills. This should also give you
You can find both of these levels in the Community Workshop from the main menu under the titles Kill 10000 Enemies (part 1) and Kill 10000 Enemies (part 2). If you click on the search bar at the top and search for the text "achievement", they should be right at the top as well. They will each take a few minutes as there's a limit on how many zombies can be spawned in at once, but there should hopefully be more than enough ammo and health packs to keep you going as they slowly trickle in right in front of where you spawn. I don't think you need to actually finish a level for progress to count, but just in case, I put a door with an exit in the back left corner of the room for when you're done slaughtering.

It is worth noting that I believe only your best run (i.e. most kills) per level will count towards the achievement, hence why I uploaded multiple maps, so you may need to play through a few more levels even after finishing both the ones I uploaded. I'm not certain though, so please correct me if I'm wrong.

Either way, as long as you kill all the zombies in both levels in one runthrough, you should only need around 500 kills max, which you should be able to get within the first few levels of the campaign without even really trying.