This should come naturally as you play. On the ultraviolence difficulty you should have come across every enemy there is by the middle of Map11, as there are no special secret blue enemies in the secret maps, and the final boss doesn’t count.
However, what may not be obvious, the game needs to register the enemies as killed by the player! So, if you do like I did and let the ceiling crushers and enemy infighting do the killing for you, the kills don’t register. For example, in Map06 (Crusher), on UV difficulty, you can let a certain enemy be killed by a ceiling crusher, and the next opportunity to kill that particular enemy comes as late as Map20, which is where I finally got the achievement.
Here’s checklist for enemies, in order of appearance (according to my memory) on the Ultraviolence difficulty.
1. Pistol zombie
2. Shotgun zombie
3. Chaingun zombie
4. Imp (brown fireball guys)
5. Demon (pink pig)
6. Spectre (invisible pink pig)
7. Lost soul (flaming skulls, although I’m not sure if these count, but you’ll surely be killing these).
8. Cacodemon (floating tomatoes)
9. Hell knights (goats who say ”aurora” when they die)
10. Revenant (skeleton guys)
11. Spider mastermind (big spiders). You’ll first meet this guy on Map06 (UV).
12. Arachnotrons (small spiders)
13. Mancubus (fat guys who say ”cannibael-o”)
14. Baron of Hell (stronger goats)
15. Cyberdemon (the big goat with rocket launcher). You’ll first see these in Map08.
16. Pain Elemental (floating moldy potatoes who spit lost souls at you).
17. Archvile (skinny guys who use magic at you and say ”Avatar!” when they die). You’ll meet first of these guys in Map11 (UV).
Edit 22/03/2020: There has been an update at some point after the launch that restored the secret level exclusive enemies to the game. So, if the achievement hasn't popped by level 20 or so, try level selecting the level 32 (the final secret level) to get
18. Blue guys from time before 1993.
If someone can confirm these enemies are required for the achievement, I'll edit the solution further.
In any case, with the help of level select, which also was added in the update, you can use warp to mop up any remaining kills. Level 20 contains both likely missables, Cyberdemon and Spider mastermind, so warp there, arm up as best you can and enter the fray.