The final stage, all it is is 3 boss fights. Just climb straight up, it doesn't matter where you exit the climb, the cutscene starts with or without you in position at the left.
any% fights Edit
There are two ways to fight the dog. The traditional, fairly safe method just uses ice the entire time, and has few guidelines to it. Open the fight with an ice shot, then turn left and fire another ice shot which will hit the dog on the wall, then fire another shot to the right. From there, it's just reading the dog's behavior and dodging while firing more ice. If it shoots fire, get away from the dog to dodge, or jump in place to dodge. If it shoots spark balls, get close to the dog and you can go underneath all of them. If he walks, you can just hop over him.
The faster way to fight the dog is to do the hetdog. Get a full charge during the climb, and when the dog's health bar is almost full (3 or so hp remaining to be filled) hold dash and shoot. This buffers a dash shot for the very start of the fight while preserving your charge shot. Then, swap to ice and fire a charged shot in the path of the dog and head to the right side of the screen. On the way, fire an uncharged ice shot into the wall which will hit the dog as a ricocheted shot. You want to end up in the corner with the dog a short distance away from you. Depending on luck, you can possibly kill the dog outright from standing right in the corner and never getting hit.
It doesn't make a big difference where you are when you kill the dog, even having to walk all the way across the room only delays the cutscene from starting by 3 frames.
The jedi Sigma fight is a straightforward fight, but Sigma does a ton of damage so it can be unforgiving of movement mistakes. Missing shots isn't a big deal as long as you keep Sigma stuck in the same movements in the same way.
If you're above him, on the wall, he'll go back and forth along the walls starting from whichever side of him you were on when he started. This means that if you're directly above him on the wall and wallkick out a little bit, you can get him to jump right first, this is bad.
Start the fight with an uncharged spark for a free hit, then go immediately to the left wall and climb. Fire a shot into the wall and get back to the wall right before he chooses to jump left or right to force him to go left. Your shot will hit him, then just stay on the wall and shoot sparks that he runs into. To avoid shooting a spark into the wall that won't hit him, you can dash wallkick from the wall before shooting, this will give a little more space and leniency to fire the shot so it can hit him. You can hit him 3 times on the way up, once at the bottom, and 2 during the climb. Then, drop down and hit him twice as he comes down. You can shoot him off the wall as he comes down, or you can shoot him directly. Shooting him directly is slightly faster in the end if you don't miss any shots, since you'll be hitting him while he's across the screen rather than flush with the left wall.
For maximum swag, after killing jedi Sigma, press weapon swap left along with the music that plays introducing the final boss. It will leave you on its weakness, rolling shield.
Wolf Sigma Edit
There isn't a lot to tell about the final boss, it isn't flowcharted so conveniently like Sigma. There's just some general advice for fighting the fianl boss.. Start by going to the left wall, but don't immediately jump up. Wait a very short amount of time, just long enough to identify if it's stopping or continuing to rotate. If it stops, then you can't climb on top of it, but if it's just rotating then you're free to climb. When you're on the paw, stand on the edge so that the lightning attack will miss you. When you're on the paws, never touch the dash button. You don't need speed, you need control, you need to control carefully where you jump to shoot the head, and where you land afterward. Only dash if you need it to bail out when the other paw comes over high and you're afraid of a lightning attack. Likewise, only go to the left wall if it's absolutely necessary. Sticking to the left wall is a good way to get hit a lot during the fight. If you've been hit by anything at all so far in this stage, one lightning attack will kill you in low%. Just stay calm, stay on the paws, and keep getting hits in. It will take a lot of practice to get good at the fight in low%, this fight is the reason some people go for the armor in any%.
100% fights Edit
Shoot a hadouken when the dog jumps off the wall so the dog lands on it directly.
You can buffer a hadouken on jedi Sigma, or do the input after the music transitions, or even as he starts moving.
The final boss itself is immune to the hadouken, so your only option is rolling shield. The same advice from any% still applies, only the fight as a whole is a lot more lenient, since you have twice the health and take half the damage.