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