There is a fifth phase if you fight him after beating Inkmatas

Phase one, he uses the Phaseslayer, this music plays: For the solar soul (For the dark soul)
Phase two, he gets more serious and pulls out the Muramasa, this music plays: Main Solar flare (Dark souls 3 main menu)
Phase 3, he pulls out the Ankh shield and gets more serious, this music plays: Solar mind (Razormind)
Phase 4, he pulls out Gael's greatsword, he is able to one hand the greatsword while using Muramasa, this music plays: The final Terrarian (Ragadon of the golden order, Elden ring)

He has a fifth phase that happens when you defeat Inkmatas before fighting Xander, in the fifth phase he channels the power of the dark soul making phase 5 a Melina level difficult phase, this music plays: Solar knight Xander (Slave knight Gael's theme)

When the boss loses health but somehow gets stronger:

When the boss bar shoots back to full: