Phase 1: Painting Attack
Phantom Ganon will ride out of one of the paintings in the room. Watch for the painting that glows. As he emerges, shoot him with your Fairy Bow. If two Phantoms emerge, shoot the one that is more solid. If you hit the wrong one, it will disappear. Repeat until he falls off his horse.
Phase 2: Energy Ball Deflection
Phantom Ganon will now float in the air and fire energy balls. Deflect his energy balls back at him with your Master Sword. He will deflect them back, creating a tennis-like volley. Keep deflecting until he is hit and stunned. When stunned, attack him with your sword. Repeat until defeated.