Painkiller Hell Damnation

This will be your last achievement and with no way of checking how many Stakeguns kills you've got it might take 10 minutes or 10 years. I'm ignoring Survival mode kills as the counter seems to be glitched (see my solution for 1000 kills).

I've been using a Load Last Checkpoint exploit which might help - running approx 1800 kills an hour. You could abuse any checkpoint but here's what I've been doing.

Set up an SP game on Colosseum on Daydream using:-
Gold Tarot - Dexterity (2x reload), Rage (4x damage), Iron Will (invincible)
Silver Tarot - Mercy (use Gold 3 times), Replenish (double ammo)

Work through the level until you get to the room with the "swimming pool" (there's a checkpoint right outside). Run in, spawn the enemies, back into a corner and active your Gold Tarot. The enemies will swarm you, hold RT for rapid fire Stakegun and you should nail 20/25 enemies in about 30 seconds. As soon as the Tarot runs out hit Start and reload last checkpoint. You'll be back outside the room, run in and repeat ad nauseum.

I timed 154 kills & 164 kills in 5 minutes using this method. It would obviously work on any checkpoint in the game so experiment!

EDIT - so finally popped the achievement. My stats...I played through the game 3 times (Daydream, Nightmare, Trauma) completing 63 Campaign maps (which might include 10 levels of co-op) using the stakegun as much as possible, then 1000 kills in Survival with Stakegun (although not sure these count cause the Leaderboards acutally show around 1700 kills!). I clocked up just over 3000 kills using the method above. Total kills 17,775.

This solution is the result of the experimentation suggestion in the solution by HWNDarkside. The important details are bold.

The strategy is the same for this solution but makes use of an exploit and more enemies per repetition.

The general strategy is spawn the enemies, back yourself into a small corner, and then become a Stakegun adept (skill not actually required).

Level select Colosseum on Daydream with Gold Tarot card "Dexterity" & Silver Tarot card "Replenish".

The other cards don't matter but Silver Tarot card "Mercy" is recommended.

Play through the level and acquire Stakegun ammo until you can begin the fight in the actual Colosseum.

Note: Save your Stakegun ammo for the arena; you don't want to be short of ammo when you activate the checkpoint you'll be reloading.

Upon entering the Colosseum and looking straight back & slightly to the right, notice a dark gate. Proceed towards the gate and notice the 3 Stakegun ammo pickups nearby. Once at the gate, back yourself into the right-side, that is, when you turn around to face the center of the arena, you'll be on the left-side.

Turn around, play your Tarot cards (X button), and hold the primary fire trigger. Once the Dexterity card is played and primary fire is engaged, the rate of fire will not revert until you run out of ammo.

Combine the card exploit with predictable AI routing (even more predictable when you're backed into a corner) and you should have a situation you can grind.

I tried a few different corners to check the enemy routing patterns but the mentioned corner proved easiest to setup.

Tips:
Pickup more ammo when you have ~15 stakes remaining.
There are 2 (generic) Ammo Packs on the right side of the arena.
Some enemies carry shields; avoid aiming at shields (easier claimed than practiced).
When you can't see, aim down a bit and use an alternating left-right pattern. (Sometimes it sounds like you're landing a hit but you can stake corpses to no advantage.)
Sometimes engaging primary fire will not yield the expected rate of fire; switch to another weapon and then back to fix the "jam".

Overall, i'm not sure about kill rate but the advantage in this solution is less reload of the checkpoint and more enemies to grind. Disadvantages are waiting for the arena door to open and crossing to the other side of the arena.

At first, I tried to maximize usage of the ammo available. After many repetitions, i settled for simply expending my available ammo at checkpoint load and then only picking up ammo once.

It's a grind but at least there is the benefit of aiming practice. I played a few hours sporadically over a few days.

Final kill count after all campaign and survival achievements: 18,528