This is pretty straight forward. You will encounter every common enemy just by playing normally.
You will need to glory kill (right stick when enemy is stunned) the following enemies:
Baron of Hell
Possessed Engineer (guy with explosive tank on it)
Possessed Security (guy with shield)
The last enemy you will need to glory kill for this achievement is "Pinky
", and you will encounter it for the first time on the 7th mission "Hell on Mars/Argent Facility (Destroyed)
The Lost Soul (flying skulls) don't count because you can not glory kill them.
You can always check how many glory kills you have for each enemy by going to the Codex-section in the menus.
-> Codex -> Monsters.
Any questions? Feel free to ask! :)