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 a 'Fun' Level
Locate the secret level 'Hectic'
Finish the Lost Levels mission
Defeat the Mother of All Demons on The Absolution
Finish 'No Escape' on Watch Me Die skill level
Acquire all 3 Demon Key Artifacts in the main campaign
Kill a Cyberdemon
Find the BFG9000
Find the Unmaker
Discover a secret area