Here is the full list of all 33 DOOM + DOOM II achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Get 25 kills with your Fists in a single level.
Get 100 Chainsaw kills.
Finish off a Cyberdemon with the Pistol.
Get 3 multi-kills with the Shotgun.
Kill 4 enemies in 1 shot with the Super Shotgun.
Shoot 200 bullets consecutively with the Chaingun.
Gib three or more enemies with a single rocket explosion.
Kill 5 enemies in 5 seconds with the Plasma Rifle.
Kill only a single enemy with a BFG9000 blast.
Kill 2 enemies with a single barrel explosion.
Crush a corpse in a door.
Finish a level with 200% armor and 200% health.
Kill one of every enemy.
Cause an enemy to kill another enemy.
Complete a level on Nightmare difficulty.
Finish a level with 100% items picked up.
Complete any monster-filled level with 100% kills without taking any damage on Ultra-Violence or higher.
Find a secret area.
Find a secret level.
Kill all monsters in any monster-filled level on 'Hurt me plenty' or higher.
Complete any monster-filled level with 100% kills, items, and secrets.
Get 20 kills using the berserk powerup in a single level.
Complete 8 different levels sequentially under par time without dying on Ultra-Violence or higher.
Immolate a total of 30 arachnoid enemies with the Incinerator.
Obliterate 50 enemies with a single shot of the Calamity Blade.
Reach the end of 'DOOM'.
Reach the end of 'Sigil'.
Reach the end of 'DOOM II'.
Reach the end of 'No Rest for the Living'.
Reach the end of 'Master Levels for DOOM II'.
Reach the end of 'TNT: Evilution'.
Reach the end of 'The Plutonia Experiment'.
Reach the end of 'Legacy of Rust'.