Alright, now, onto this battle...
This is honestly really difficult. Kiir has the ability of knowing all of Apeiros' moves before she uses them, and considering Apeiros' character, she doesn't bust out her intense hax until after realizing how ineffective her regular ones are at the start. The difference here is that after a bit of fighting with eachother and Apeiros getting annoyed by Kiir's abilities, she could do a number of things to her such as Mind Hax or nullify all of her supernatural powers via how her PN works. It comes from a 3-C being and, considering it acts like a miniature form of how a
certain guys PN works, would be a problem for Kiir as Apeiros is indeed no stranger to really unconventional fighting styles considering she won a match against Georgie Small who is kind of like Kiir in how she fights like how he is constantly moving and performing plenty of flashy flips and kicks in battle, generally being very unpredictable.
But I'm not saying Kiir wouldn't have any way of beating Apeiros. Despite that range advantage Apeiros has, Kiir's Reality Manipulation can close a gap and if Apeiros is not careful, she can get tricked and very well can be defeated that way, and again, considering Kiir's precognition, she could definitely play around and stay out of range of Apeiros' more deadly and devastating hax, so if she plays it
just right, she can get a win. Another thing is her probability manipulation could indeed mess Apeiros up quite a bit. Also, assuming Apeiros had not slept in a bed, her Low-Godly Regen would only be mid and she would not have Type 8 immortality.
All in all, I'm voting inconclusive. Kiir has a few ways to mess Apeiros up, but Apeiros' hax and range advantage she has is quite deadly and she could pull through as well. Considering she is an excellent planner and thinker, Kiir will have to think carefully as well on all the possible powers Apeiros has up her arsenal she can use against her that would be detrimental in the end. It's kind of like An Unstoppable Force (Apeiros) vs. An Immovable Object (Kiir). Apeiros has all of those hax and abilities up her sleeve while Kiir knows all of her hax and abilities that can be used against her, but the question is, what will they do to beat one another to get passed these abilities that can counter eachother? It's hard to really tell so that's why I vote inconclusive.
On a side note, I really like the dynamic in character within this battle because of that among other reasons. Their philosophies seemingly clash perfectly. Apeiros hated her mortality and wanted to rise farther passed it, as well as everyone else, gaining more powerful as a result, while Kiir, on the other hand, felt lonely at first simply because she was one of the most powerful fighters on Gyrohem and being above most others, which contrasts well in this dynamic. The One who was trying to reach seemingly impossible levels of power vs. The One who was pretty much already there compared to most others, but had developed more with the people she met. An interesting thing to note is Apeiros kind of has another version of this. When asked by Georgie Small (who she had been developing feelings for) if she would even sacrifice him to reach her goals, she just remained silent and contemplated it. Both had experiences with others that made them develop something else and not be so singleminded, just in different ways. I'm really sorry, but I just noticed this worked really well as a Good vs. Evil dynamic and I found it quite interesting ^^'