This...questionable achievement requires a bit of set up to do without grinding for hundreds of hours. First off, I'd estimate there is an average of 50 enemies per level (later missions have more, earlier ones have fewer) and you'll encounter 50-75% of them going for objectives normally. Enemies don't respawn and you only get credit for kills by saving and exiting a level so normal save-scumming is impossible. After getting all the other achievements (14 missions + 12 for getting all influence techs + 1 for strip mining) you will probably only have around 27*50*0.7 = ~1000 enemies killed, maybe up to 1500 if you go out of your way to open up every room and kill everything. Even worse is the fact that there's no tracker to tell how far along you are.
The fastest strategy I found to grind this is the following:
1. Reset the Infested Mountain (it seems to have the most enemies, around 100).
2. Avoid opening any unexplored rooms and mine and expand until you have upgraded your spawn pool to max, recruited as many dwarves as possible, researched every tech, turned as many dwarves as possible into warriors (all but 4 workers, 4 diggers, and 1-2 craftsmen), and upgraded every warrior to at least level 10 and specialized them.
3. Dig single-width tunnels up to but not opening every room you can find. Try to have the tunnels go up to the lowest level of the unopened room.
4. Wall in your prince with with a bed and dining table
5. Ensure there is only one vertical tunnel leading above and below your main base (tunnels can branch off of this as much as you want. Make sure this tunnel is walled off with at least 5-6 layers of the strongest walls with only your diggers outside of it (2 above and 2 below)
6. Pause your game and set a dig order to open up every room. You might want to avoid the room with the queen spider (very large room near the bottom of the level) to avoid the cutscenes as there's only 5-6 enemies there.
7. Unpause until your diggers open up every room in the level. They should hopefully survive long enough to open them all. If not, just train more and teleport them outside your walls. The walls should hold long enough to do so.
8. Once every room is opened, pause your game and delete all the walls between your main base and the rest of the level. Then save and exit without unpausing.
9. Make sure cloud saves are disabled and navigate to the save game folder. It should be located in C:\Users\your user name\AppData\Roaming\Zeal Game Studios
10. Create a second folder (I named mine "backup_saves") and copy and paste all the save games to it.
11. Launch the game again, unpause, and wait for all the enemies to be killed.
12. Save and exit the level
13. Close the game, navigate to the save folder, delete all saves, and copy your backup saves to it.
14. Repeat 11-13 until the achievement unlocks, around 90 times.
Steps 11-13 take around 6-7 minutes each time so you're looking at 8-10 hours to grind this out. You can make this less of a nightmare by using an autoclicker to repeat the steps. I set one up before going to bed and it had unlocked when I checked it a couple hours after waking up.