All easier strats will be covered in the beginner's guide
This guide is all about the advanced strats used in the final showdown with Axel which consists of 3 Phases.
[big]PHASE 1:[/big]
This phase can be handled in 2 different ways; each with a few drawbacks from the other.
This method shown above is a fairly consistent strat where you string a few consecutive hits on Axel and then exchange hits and then repeat this process. The drawback of this strat is that you are forced to end this phase with just 2 hearts remaining. In tandem with the additional heart lost from Phase 3 (more on that below), this leaves you with a single heart remaining to get through both the Hell room (arguably the hardest room in the game) and the final boss.
It is also the slower of the 2 potential quick kills in this phase though not by as much as once believed.
Unquestionably considered the hardest strat in the game to pull off, the "TAS Axel strat" as I call it is a wildcard of a strat where the idea behind it is to chain hit after hit to create a stunlock on Axel. Each of these hits is a 2 frame window, but there is a 3rd frame of generosity where you won't land a hit but prevent getting hit by Axel. Instead you will clash with Axel's sword/projectile. This happens because you pressed attack one frame too early from the 2-frame window.
But what makes this strat so brutal isn't just the small frame window for every hit but also the need to change positioning throughout this phase of the fight. For every single successful hit on Axel, he will move a few pixels to the left. This is very important to understand as by not maintaining the correct distance from Axel, one really bad outcome can happen which by itself can nullify the entire time saving advantage of this strat by itself.
Let's (for example) say you successfully keeping landing the 2-frame window consecutively but you don't move at all. What will end up happening is Axel will eventually get far enough away where one of your sword swings will outright whiff and more than likely Axel will land a hit on you. If he does hit you in this situation he will proceed to do the absolute worst thing and that is jump to the other side of the room before eventually jumping back to the corner where you want him.
That's what happens when you allow Axel to get too far away. So what happens if you are too close to him? Well in that case, the 2 frame window becomes a 0 frame window and the best outcome is to exchange hits pretty much exactly like the other quick kill strat. The consolation for being too close to Axel is that he at least stays in the corner so the time loss is very minimal.
In short, it's much better to mess up this strat by being too close to him than being too far away.
[big]PHASE 2:[/big]
Thankfully Phase 2 is much quicker to understand.
-First you'll want to get up to the ceiling.
-After that, tap left once to cling to the middle bar. Then tap and hold left to go from the middle bar to the bar closest to the void of space and stay there. Do not move yourself up at all during this.
-Wait until Axel hits this point indicated in the picture below:
-Once he does hit that point, rocket boost right into him (this is why you hold left in the previous steps).
-You will then ricochet to the middle bar. From there, slash him with the base sword twice and throw one more slash to hit him with the projectile.
-With the third slash, begin holding attack and once you've confirmed the projectile hits Axel, move down to meet up with him and rocket boost down and straight into him.
If done right, it should look like this:
[big]PHASE 3:[/big]
The first major thing many people may not realize is that by moving Sparkster as far down as possible and then back up, you actually manipulate the camera to see more of the area up top. Doing this simple thing is what allows me to setup for the quick kill of the 3rd and final phase of this fight using a particular visual cue.
In the above image, I use a part of the background as my visual cue of where to stay and wait for Axel. I edited a small little yellow line of the spot I'm referring to here. Using that, I line up Sparkster so that both his hands clinging to the bar and his ears align on both sides of it.
As for when I rocket boost into Axel, I wait until his ears cross with an identical looking visual cue (just in a different spot). The white arrow should indicate what I'm talking about here.
The idea of the quick kill for this phase is to hit him with the rocket boost but ricochet past him and arc around to the very top. From there, you wait until Axel runs into you which should knock you to the middle bar. Then, whilst holding Right so that you don't move to the left bar, 2 sword slashes from there should deal the finishing blow (throw a 3rd slash if you're unsure).
It should look somewhat like this: