Here is the full list of all 10 DOOM 64 achievements. It takes around 1-2 hours to unlock all of the achievements on Windows.
Finish the Lost Levels mission
Finish a 'Fun' Level
Acquire all 3 Demon Key Artifacts in the main campaign
Locate the secret level 'Hectic'
Defeat the Mother of All Demons on The Absolution
Finish 'No Escape' on Watch Me Die skill level
Kill a Cyberdemon
Find the Unmaker
Find the BFG9000
Discover a secret area