The best way to fight each phase is dependent upon the category you're running and what equipment you have.
Mask hovers around the room and has two attacks:
The boss remains begin flying around the arena partway through the Mask fight and can shoot Link with light balls.
See second half of video for steps and visual cues.
Stun with a sword beam, then jumpslash and back away before the cutscene. Stun with another sword beam and hit with another sword beam. Before the transition to Incarnation begins, you can turn around and try to hit one or more of the remains with sword beams.
A bomb exploding in the center of the room will always knock Incarnation down. Otherwise, its actions are erratic and include moonwalking, a light ball attack, pretending to trip, and sprinting.
Stun with a sword beam, then spam sword beams.
Wrath can dodge or block most attacks, but it never dodges a light arrow shot, even if you're out of magic and Link only fires a normal arrow.
The simplest tactic is to stun Majora with a sword beam, then land 5 jumpslashes with animation cancels. The strategy in the video below is faster and more complex, and is explained in detail in the video.
This video demonstrates the fast strategy with input display.