Like all humans, Ashikaga Takauji ignores Elbereth; while his attacks are normally unimpressive, he has two weapon attacks and will wield your quest artifact against you, possibly bisecting and killing you in one hit. This and his base AC of 0 makes him one of the most dangerous quest nemeses to face in melee range, and there is no shame in considering leaving Takauji alone unless you have options to actually deal with him; more cautious players may wait until they have a more thoroughly assembled kit with a fallback measure, usually an amulet of life saving. That said, the quest itself offers plentiful numbers of attack wands that can make the encounter much easier, especially combined with a scroll of scare monster.
It is very easy to approach Ashikaga Takauji without disturbing him from his meditation, due to the layout of the level; the final entrance before the inner section gives you a clear shot with any ranged weapon or wand, while still being far enough that he will not wake up. He has no elemental immunities and only moderate magic resistance, so the wand of death can put an end to him immediately, and any attack wand that hits will do enough damage for him to immediately flee to the up staircase, ignoring the Tsurugi. You can use this opportunity to pick up and stash the Tsurugi before he can return, making him relatively trivial to defeat; you can also leave a powerful pet near the upstairs to finish him off as he tries to heal.
A wand of sleep may also work, but carries the risk that his magic resistance will allow him to resist the ray, possibly waking him up and giving him a chance swing the Tsurugi at you. If you take this route, it is strongly recommended to wear an amulet of lifesaving before engaging, to reduce the risk of YASD to an unlucky Tsurugi hit.
An alternative strategy is to polymorph into any monster of large size or bigger to avoid the risk of being bisected; polymorphing into a black dragon adds the ability to kill Ashikaga Takauji instantly with disintegration breath via the #monster command, and neither the Tsurugi nor the Bell of Opening will be harmed.
If needed, the disarm technique can get Ashikaga to drop the Tsurugi with fairly decent frequency, just in case a melee fight is unavoidable. One can then hit him, to make him teleport to the stairs and heal, leaving the Tsurugi behind.
Ashikaga Takauji was an historical figure of medieval Japan. He was Shogun from 1338 to 1358.
Ashikaga Takauji was a daimyo of the Minamoto clan who
joined forces with the Go-Daigo to defeat the Hojo armies.
Later when Go-Daigo attempted to reduce the powers of the
samurai clans he rebelled against him. He defeated Go-
Daigo and established the emperor Komyo on the throne.
Go-Daigo eventually escaped and established another
government in the town of Yoshino. This period of dual
governments was known as the Nambokucho.
[ Samurai - The Story of a Warrior Tradition, by Cook ]
On July 8, 1336, he and his samurai entered Kyoto, forced Go-Daigo
to retire, after which he seized power himself and installed a
puppet prince on the throne (the current Japanese imperial family
are the descendants of this puppet emperor that Ashikaga
Go-Daigo escaped, though, wouldn't admit to have been defeated,
and opened a new "capital" in Yoshino (south of Kyoto), where he
and few of his descendants claimed to be running a government,
known as the "Southern Court". The period between 1337 and 1392,
when Japan was ruled by two courts, is known as the Nambokucho.
That "government" disappeared, naturally, after a few generations,
and Ashikaga's Muromachi regime lasted for a long time. The last
Ashikaga daimyo in power was the 14th descendant of Takauji.