Here is the full list of all 20 DOOM (1993) trophies - there are 5 bronze, 6 silver, 8 gold and 1 platinum.
Unlock all trophies in DOOM
Beat DOOM in under 2 hours
Finish off a Cyberdemon with the pistol
Find all the secret levels
Kill one of every enemy
Beat all the levels in "Thy Flesh Consumed"
Get 100 kills in deathmatch
Get 25 kills in deathmatch
Get 25 kills with your fists in a single level
Beat all the levels in "Inferno"
Beat every level on Nightmare in co-operative mode
Kill only a single enemy with a shot from the BFG
Beat all the levels in "The Shores of Hell"
Find a secret level
Kill 5 enemies in 5 seconds with the plasma rifle
Beat all the levels in "Knee-Deep in the Dead"
Get 3 multi-kills with the shotgun
Crush a corpse in a door
Kill 2 enemies with a single barrel explosion
Finish a level with 200% armor and 200% health