Optional: Demon Prince
Maximum souls: 743,580
The boss is vulnerable to bleed in both phases 1 and 2. Consider using a blood infused weapon such as Blood Warden Twinblades+10 or Blood Bandit's Knife+10. If using the Blood Warden Twinblades+10, two-hand the weapon and get in 1 or 2 L1. The one-handed R1 of the Blood Bandit's Knife+10 has a fast recovery time, allowing you to spam R1. Equip the Flame Stoneplate Ring+2 and consume a Red Bug Pellet to boost your fire defense. Consider equipping a blessed infused Caestus+10 in the left hand and the Sun Princess Ring to help with your HP regeneration during the fight. For extra safety, cast Tears of Denial before entering the boss arena.
In phase 1, ensure you defeat the Demon in Pain first. This would allow for an easier 2nd phase. Try to always have both demons in view. Get in a hit or two, and dodge any attacks.
At the start of phase 2, quickly buff yourself with Sacred Oath and consume a Red Bug Pellet. Wait for the explosion to take effect, sprint to the boss, and get in 1 or 2 hits. As the boss flies away from you to throw a fireball, lock onto the boss and sprint to it to dodge the fireball. Also, when the boss charges up a burst of wind, release the burst of wind, and flies backward, as soon as you see the wind being charged up, roll into it and sprint in the direction that the boss is flying. Once the boss is on the ground, run behind it and spam as many hits as possible. Refer to the following video for the bleed strategy.
Demon Prince NG+32 Warden Twinblades, Dark Souls III
Gael and Lapp are available to be summoned. You can summon one or both to help you distract the Demon from Below while you fight the Demon in Pain. No matter what you do, ensure the Demon in Pain is defeated first. If you only want one phantom, Lapp is the better choice because he is more of a tank than Gael. Most of the time, it's easy to get Gael and Lapp to distract and defeat the Demon in Pain while you fight the Demon from Below. Be sure to pay attention to the HP bar of the Demon in Pain to make sure you don't accidentally kill the Demon from Below first. Gael and Lapp are meant to help you distract one demon while you deal with the other demon. During the 2nd phase, the NPCs are more useful as a way to chip down the boss' HP bar and they would likely die during this phase.
Demon Prince NG+34 co-op, Dark Souls III
This video contains a detailed strategy:
Demon in Pain & From Below Boss MADE EASY - Dark Souls 3 Ringed City DLC - Solo NG+7