Demogorgon

Demogorgon is the toughest monster in the game. He has four attacks: A spell for 8d6, a sting attack that drains a level, and two claw attacks for 1d6 plus disease.

The only way to survive Demogorgon is to be prepared. Be very fast and unburdened, capable of curing diseases, and be able to attack him. Magic resistance and cancellation go without saying. Generally, you will need speed boots or haste self, and either a unicorn horn or Staff of Aesculapius for equipment.

As for how to actually kill him, there are several ways. First, you can beat him to death, but this is very slow and difficult to do. He is not immune to stoning or disintegration, so you can kill him in that manner; if you have any wishes left, wishing for a cockatrice corpse could be a really good idea. If you can reach the up-stairs first and engrave Elbereth there, you can beat on him freely with no risk of illness. Finally, if you can, GET AWAY! Leave immediately and get past him. Teleport to the staircase, zap a wand of digging downwards, quaff a cursed potion of gain level. Discretion is the better part of valor.