158 Damage
Assailant
Classes
The base of this build is a Paladin/Rogue multiclass. We're going to be combining the Assassin Rogue's ability to get guaranteed critical hits, and the Paladin's Smite - neither of which require a weapon.
Paladin 13 gives us access to a 4th level Divine Smite (5d8), and to Wrathful Smite (1d6) (the only Smite spell that does not need a weapon). As one of their ASIs we take the Alert feat, giving us +5 to initiative rolls.
Rogue (Assassin) 3 gives us access to Assassinate, which guarantees a critical hit on a surprised enemy which has not taken their turn yet. (And Expertise in Stealth to guarantee surprise)
Monk (Four Elements) 3 gives us d4s for unarmed strikes, and Fangs of the Fire Snake, another 1d10 damage. Also the ability to use Dexerity for our unarmed damage rolls.
Items
Insignia of Claws gives +1 to the damage of Unarmed Strikes.
Enough Manuals of Quickness of Action to get this character to 30 Dexterity.
Damage (no helper)
So let's see how much we can do without our helper.
First we stealth up to our target and surprise them with our +22 to Stealth from expertise alone. Having remained undetected, we jump out. They are surprised. We roll initiative. We have +15 to initiative rolls, so should hopefully be able to beat them. Assuming we do, our attacks against them will be criticals. We cast Wrathful Smite with a bonus action, walk up to them, and hit them with our fist, burning a 4th level spell slot for a Divine Smite, and 2 Ki points to deal +1d10 damage with Fangs of the Fire Snake.
10 {Dexterity} + 1 {Insignia of Claws} + (1d4 {Monk unarmed die} + 5d8 {4th level Divine Smite} + 1d6 {Wrathful Smite} + 1d10 {Fangs of the Fire Snake}) * 2 {Critical hit from Assassinate}
= 79 damage
Helper
Our helper is a Cleric (Grave Domain) 2. They use their Channel Divinity: Path to the Grave feature to give this creature vulnerability to all the damage of the assailant's next attack. This doubles the damage above.