This video is tool-assisted. http://tasvideos.org/
If you've seen the early power bombs video, this video uses the same method to access part of Sector 5 early. This lets you fight Nightmare early. However, you won't obtain the gravity suit, and the game will tell you that level 3 doors are unlocked (though it doesn't actually unlock anything).
If you enter Nightmare's room, you'll get stuck since you need gravity suit to leave. The enemies can't be used to get out of bounds.
Also, Nightmare will always respawn as long as the player doesn't have gravity suit.