Here is a video on how to obtain the achievements, My Cause is Just, My Will is Strong, Unholy Firepower, and Mother May I?
To easily unlock these achievements enter the ultimate Doom 64 cheat code (W93M 7H20 BCY0 PSVB) in the menus to start the level. Before leaving the room, fire a shot of your BFG and Unmaker to be able to pick up new versions of these guns and unlock the corresponding achievements. Once done pick up the invulnerability sphere and head into the large room. and quickly hit the three switches to seal the small structures around the room. pick off any monster that spawned in, the demon mother should appear in the centre platform. Switch to the Unmaker and unload on her until she is dead.