Optional: Old Demon King
Maximum souls: 278,842
All demon bosses are weak against dark damage. These include the Old Demon King, the Stray Demon atop Farron Keep, the Demon who guards the entrance to Smouldering Lake, and the Demon in the Undead Settlement. The Demon in Pain and Demon from Below are both weak against dark, but the Demon Prince is resilient against this elemental damage.
Equip the Court Sorcerer's Staff+10 (or Murky Longstaff+10) in the left hand and equip the Scholar's Candlestick+0 in the right hand. Equip these to boost your damage output: Blindfold Mask, Dark Clutch Ring, Young Dragon Ring, Bellowing Dragoncrest Ring. The 4th ring can be either Chloranthy Ring+3 or Lloyd's Sword Ring. Use the weapon art of the staff to buff it and cast Affinity. Cast Great Soul Dregs as your primary offensive weapon. The video below demonstrates the dark sorcery strategy.
Old Demon King NG+32 dark sorcery, Dark Souls III
If you defeated Tsorig while he invaded you at the Catacombs of Carthus, you have the choice to summon him for this fight. You can summon Cuculus as well.
Old Demon King NG+34 co-op, Dark Souls III
Refer to this guide for more details on dark sorcery:
https://steamcommunity.com/sharedfiles/filedetails/?id=2494204157