Instructions
Enter World 4-1, the Shrine of Storms, and walk up a little and to the left after defeating the first skeleton. There is a character with white hair wandering around in this area. Talk to Satsuki, and give him the Makoto sword when he asks for it. As soon as the conversation ends, he will attack, so have your shield ready, or get ready to dodge.
Dodge Satsuki's katana attacks and make your way around to his back by circle strafing. Attacking from behind will kill him quickly when he is in body form. When you return to 4-1, especially when the world is in Pure Black tendency, the fight is entirely different.
Stay near the entrance archstone of 4-1; Black Phantom Satsuki will charge you as soon as you enter the level. Equip a strong shield with as many enchantments on it as possible; the katana cannot pierce a full block from a strong shield. Quicker characters with strong shields, like thieves, are better for this fight. Although the backstab strategy still works, Satsuki is much stronger and faster than before, so you need to allow him to strike the shield to gain an opportunity to attack.