The two "heavenly" boss battles - the dragon of Fuji and Raijin. The only comparable battle in any other video game might be the Nine-Tailed Fox in Okami.
The boss fight with your other playable character, especially when your swords clash.
Like the heavenly battles, the fight with Inugami at the end of Kisuke's story is amazing. There is an incredible personal stake in the battle, and it begins fairly easily (and a bit disappointingly). But then the real power shows itself, and Eldritch Abomination vibes start being thrown everywhere. The entire second half of that battle was awe-inspiring.
The Bonus Dungeon Demon Trees. Several have quite a bit of challenge to them, with the most absurd being "Total Pandemonium/Night of Absolute Chaos", with a recommended level of 92 out of 99. Your reward for beating it is clothes an item that keeps your sword energy from ever dropping, making any subsequent fight a cakewalk. Though, if you can clear this, you didn't really need that anyway. Its fights are:
Waves 1 to 3: Ninja.
Wave 4: God of Pestilence, from an earlier bonus dungeon.
Wave 5: God of Pestilence(x2) and musketeers.
Wave 6: Upgraded ninjas from late in the game, who explode when killed.
Wave 7: Giant Skull Valley Ninja (x3) - Kisuke's first boss.
Wave 8: Every variant of the human Samurai enemies.
Wave 14: Pheasants and Boars from the Kai Demon Tree.
Waves 15 to 16: Tengu and upgraded (white and gray) Tengu from late in the game.
Wave 17: Yuki Onna/Snow Maidens.
Waves 18 to 19: The Phantom Samurai enemies.
Wave 20: Chigurui Bishamon.
Wave 21: Small Oni.
Wave 22: Big Oni (x2).
Wave 23: Beast Oni (x2).
Wave 24: Five Beast and Big Oni.
Wave 25: Doppelgangers: Both Momohime and Kisuke, each with an Oboro Muramasa blade, Quick Draw counter, and AI-exclusive melee spam attack.
This complete game is twice the size of Wii sports, at 0.62GB. 0.49GB of that is soundtrack.
After Jinkuro's control of her forces Momohime to take a visit into Hell, she becomes so scared that she takes control of her body again, allowing Jinkuro's soul to be eaten. To rectify the problem, she walks up to the same demon and politely requests that he swallow her whole in order to get Jinkuro back and they can fight their way out.