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 every level on Nightmare in co-operative mode
Beat DOOM in under 2 hours
Find all the secret levels
Get 25 kills with your fists in a single level
Kill 2 enemies with a single barrel explosion
Finish off a Cyberdemon with the pistol
Beat all the levels in "The Shores of Hell"
Get 25 kills in deathmatch
Get 100 kills in deathmatch
Beat all the levels in "Thy Flesh Consumed"
Find a secret level
Beat all the levels in "Inferno"
Kill one of every enemy
Kill only a single enemy with a shot from the BFG
Kill 5 enemies in 5 seconds with the plasma rifle
Crush a corpse in a door
Get 3 multi-kills with the shotgun
Finish a level with 200% armor and 200% health
Beat all the levels in "Knee-Deep in the Dead"