"I…I will find the transgressor, and I will dispatch them."
The tendril departs from his body with a nasty sh-luck!
It seems he will have to visit a clinic before this operation.
"MANY THANKS, GU'UL."

This is the start of a consistent issue in regards to formatting. There needs to be consistent spacing between these paragraphs, just as you had right before this. On top of that, I'd recommend taking a second look at what actually needs its own space between breaks rather than just being a part of a larger paragraph. Using one sentence as an entire paragraph works well for emphasis and has its function in dialogue between characters, but not everything must be separated out like that. For instance, here I would say that "The tendril departs from his body with a nasty sh-luck!" and "It seems he will have to visit a clinic before this operation." should both be together rather than apart.

Kojiro awoke in a daze. He was surrounded by… Some form of circle, with a dragonfly, kin of his own bisected in front of him.

There's a shift here and in later places to past tense, making the tense of the piece as a whole inconsistent. It'd be a good idea to go back through and comb for these inconsistencies, choose either past or present for the whole.

even after his defeat…

I'd recommend nixing the ellipsis.

seventy-three thousand nights beyond your era.

How does he know this? What are the telltale signs? Or did someone inform him? The Above? This is something of a microcosm of a larger issue I have with the piece, discussed in my general thoughts.

their clash, Gu-ul unable to gain

"Gu-ul" —> "Gu'ul"

another rooftop, and Gu-ul gives chase with a leap

Again, see above.

Gu-ul had told him that he resided

Thirded.

Kojiro had spent 4 hours wandering the streets

I've heard it said one should spell out numbers. I don't know if it's actually a hard and fast rule, but I certainly do advocate for it.

silent to the flykins' pleas

The apostrophe here should go before the s since it's a singular flykin.

Gu'ul rushes forward, through 5 strikes from Sasaki, getting within the minimum distance of his nodachi. Sasaki kicks off of Gu'ul's body, moving himself backward.

Firstly, I'll advocate once again for spelling out five.
Second, why suddenly swap whether you use his first or last name when referring to Kojiro? It only gets a little confusing and disorienting. I'd recommend keeping it consistent throughout.

So, he supposes its time.

"its" —> "it's"

Dani Gaeshi!

I dunno if this is supposed to be a confusing thing left to be unraveled later, but it certainly don't make sense now. I just felt I should make note of it and my subsequent confusion.

STAYING BY THAT USELESS MASTER, UNTIL THE END.

I'd nix the comma.

General thoughts:
Right off the bat I wanna say that I don't actually have many qualms with your combat, despite what you may think of it. I think you understand well enough the pacing and details needed for the moment to moment.

My major qualm with the piece, as poked at earlier, is that it feels like it lacks any foundation. I'm saying this very tentatively, as my recommendation isn't that you sit back and infodump worldbuilding stuff. I saw the conversation in the Discord and I agree with what was said, but you can't just go without any details at all. As of right now, the piece feels like I walked to a random book in a library and opened it up near the end. What I'm looking for is more detail in the moment to moment, of who these people are, why they're doing what they're doing. There's a taste of that with Gu'ul's memory near the end and his Above talking about a "fraying reputation", but that's about it. Of course, I could be alone in this. Uncanny said they'd crit it too, so see what they have to say. I might just be shouting at clouds.