Here is the full list of all 10 DOOM 64 achievements worth 1,000 gamerscore. It takes around 1-2 hours to unlock all of the achievements on Xbox One.
Finish 'No Escape' on Watch Me Die! skill level
Locate the secret level 'Hectic'
Acquire all 3 Demon Key Artifacts in the main campaign
Finish a 'Fun' Level
Discover a secret area
Finish the Lost Levels mission
Kill a Cyberdemon
Defeat the Mother of All Demons on The Absolution
Find the Unmaker
Find the BFG9000