Phantom Ganon is not a particularly difficult boss, however his attacks do deal a large amount of damage. While Phantom Ganon is charging up a lightning ball to throw at you run beneath him and use a quick spin to bat his attack back at him. Being beneath him, he will not be able to knock it back at you. If Phantom Ganon spawns behind Link, do a quick slash to stun him. After he is stunned in either case, wait for him to float to the ground and perform a jumpslash quickpin along with as many quickspins as you can do before he disappears and reappears.
Humorously enough, you can skip the majority of the Phantom Ganon battle in Ganon's Tower by simply knowing what doors to go through to get to the light arrow. Here is the proper order of doors in order to get to the light arrow: back, left, straight, left, right, straight. When fighting him to make the Light Arrows chest spawn you only need to stab him once to make him disappear. After obtaining the light arrow, simply shoot Phantom Ganon with one to defeat him.
Note: If the circle of fake Phantom Ganons spawn around you in either of the two battles described above, the real Phantom Ganon will always spawn directly behind Link.