I saw a group of videos in a post addressing this exact thing. I only remember the final battle from Samurai Champloo being listed as Level 10.
Now are we talking about what a fighter according to D&D rules is
at those levels, or what a fighter should be
What Fighters Are
: At levels 1-5, a credible threat to all opponents. After that, becoming more and more useless with increasingly marginal abilities that result in a Level 20 fighter being able to dish out (and take) barely more damage than a level 5 fighter, whereas his opponents can slaughter him at any level. At level 20, the 3.5 core fighter is paltry. Multiclassing (eg. into a Horizon Walker) and feats and races from outside core can fix that.
What Fighters Should Be
Level 1: Ramza the squire, at the beginning of FFT. Can take on basic enemies in groups, and other basic warriors 1 on 1.
Level 5: The Shadow of the Colossus protagonist. Can go toe-to-toe with a Dire Lion (where in RL regular lions kill people dead).
Level 10: This quote:
"I've seen this kind of fire-breathing chicken-demon before. We're going to need more rope. Also a bigger cart." Can take on dragons and 9-headed pyrohydras by himself.
Level 15: Kyoraku
. Kyoraku for a swordsman-type, Starrk for a ranged-type. (Although tbh, Bleach is kindof a bad reference because of the varying power levels, those two episodes kinda represent what I mean). Has taken down BBEGs in the past, and can single-handedly kill an full-grown dragon (who has sorcerer casting, flight, status-affecting breath-weapons, etc in addition to massive strength and more attacks per round)
Level 20: I don't know any examples for this. At this level, a fighter can take on a Tarrasque or Balor (which has crazy-powerful abilities) by himself. He's basically unkillable. Maybe the Ginyu force, for unarmed fighters, would work.
Btw, IMO the Ginyu Force was the last credible threat in DBZ before power levels went off the rails.