One of the harder quests in Nethack, because your nemesis has the Tsurugi of Muramasa and will cut you in half with it if you don't watch out. The best thing to do is to kill him with a wand of death; alternatively, I believe you can use a bullwhip to disarm him.

This quest is also a great place to observe the minor Nethack bug that if you kill your nemesis in an unusual way, the messages which the game gives may not be appropriate. Here's what happens if you polymorph into a black dragon and disintegrate him:

Ashikaga Takauji is disintegrated!

Your healing skills tell you that Ashikaga Takauji's wounds are mortal.

You know that the bushido tells you to finish him and let his kami die with honour, but the thought of so many samurai dead to the man's dishonour prevents you from giving the final blow.

You order that his unwashed head be given to the crows and his body thrown into the sea.