The best way to fight each phase is dependent upon the category you're running and what equipment you have.
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.
Stun with a sword beam, then spam sword beams.
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.