M10S - Flame Floater
At the start of this fight, each boss will attack you one at a time with their signature attacks, which allows you to understand their mechanics. Understanding what each boss is capable of will allow you to have an easier time in understanding the later mechanics, when they both attack you at the same time.
You will fight Red Hot first in this section, so get ready to pull the boss once you finish counting down. Upon pulling, this boss will do a few auto attacks into Hot Impact which is a hard hitting tankbuster that needs to be soaked by both tanks. After dealing with the tankbuster, the boss will jump to a random cardinal wall and start casting Flame Floater.
Flame Floater
Red Hot will target four random players in a specific order, the order which is also shown by their limit cut number, which he will dash into. The targeted players will get a tether that must be stretched far enough from the boss in order for the attack to be not lethal.
After every dash, the boss will leave behind a line of fire that essentially functions as a denial of area. Your goal as a party is to resolve all four dashes without hitting any other players, while also minimizing the amount of area that the boss covers in fire.
There are multiple ways of doing it, which ranges from yolo'ing it to drawing a giant square around the edge of the arena, but the PF way of doing it is to have the boss dash back and forth on the same wall it started, starting with a right dash while looking at the wall. Identify your number, and have the 1/3 preposition themselves at the right side, while 2/4 preposition themselves around the middle.
The fire on the floor will take at least 3-4 seconds before it solidifies. Until then, you can actually freely step into the fire without taking any bleed debuffs. With this knowledge in mind and if you are brazen enough, pop your sprint and feel free to try to uptime the boss while he is dashing back and forth.
As a note, avoid stretching the tether too far, because that will impact the melee's ability to uptime the boss. The boss will stop exactly at where the players are, so stretching the tether unnecessarily far will cause the boss to dash farther then what is needed. Love your melees and they will return the love by killing the boss faster for you.
Once the mechanic is resolved, pull the boss out of the fire as this allows your party to uptime the boss while preparing for the next mechanic.
Alley-oop Inferno
You have a small window before the boss locks in place and casts Alley-oop Inferno, in which he will chuck a fire AoE puddle on every player. These fire puddle will solidify and create another set of denial of area, so spread out along the walls and make sure none of the puddles drop in the middle, which is important for the next step.
Just like before in Flame Floater, the fire on the ground will take a good 3-4 seconds before it solidifies, so you can just freely walk through them during that time without any problem.
There is no priority system for this, so your eyes and common sense is applied here. Give melee the area around the boss, while the ranged goes far away, and finally, take the loss by disengaging and using your ranged attacks if you're in danger of killing your party members.
Cutback Blaze
After resolving Alley-oop Inferno, immediately have the MT drag the boss out of the fire if hes currently standing inside it. The boss will use Cutback Blaze, which is a weak raidwide by itself but it will also target the furthest player and cover the whole 330° degrees in the direction of the targeted player with fire, leaving only the area behind him safe.
As ranged, especially if you're D3, try to go out as far as you can to ensure that the safe zone is created. This will allow the melees to get their positionals by simply staying inside the boss circle.
Pyrotation
Go into the safe slice and get ready to move as one of the healers will be targeted with Pyrotation, which is a 3-hit stack marker that leaves behind a fire puddle every time.
After the third hit, the boss will wrap up this phase by casting Divers' Dare, which is the generic raidwide attack of this boss battle. This raidwide is survivable even without mitigations for now, but this will change soon as you will see later.