In Nethack, quest nemeses and demon lords are difficult to kill because they keep teleporting away to heal themselves. If you can't kill them instantly (for example, with a wand of death or a cockatrice corpse), you need to find a way to make them stand still and fight you.

The technique for doing this is known as the upstairs/downstairs trick. It begins with noticing that these monsters teleport to the up staircase. If you can get there before they do, they won't teleport away. If you can't, you'll need to exploit another feature of these monsters: they'll follow you up or down stairs if they are next to you. This enables the following strategy:

  1. Head for the nearest staircase. If the monster is there, fight him until he moves away. If he goes up or down the stairs, follow him. Otherwise, just occupy the staircase yourself.
  2. You should now be on a staircase on the same level as the monster. If it's an up staircase, you're done - he can't teleport away, so just kill him.
  3. If it's a down staircase, wait for the monster to come back. As soon as he's next to you, go downstairs.
  4. If you're on the up staircase now, fine. If not, go back to step 1 - fight the monster until he either moves away from the staircase or runs up it.

Sadly, this technique does not work against master liches and arch-liches, because they do not follow you up or down stairs. I'd advise genociding them or petrifying them with cockatrice eggs.

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