Demon Prince

The Demon Prince is a boss in Dark Souls III: The Ringed City.

Description
The fight starts with two active bosses, Demon in Pain and Demon from Below. Both periodically ignite and extinguish, using different abilities depending on which of the two states they're in. After killing them, the demon who died last sprouts wings and becomes the Demon Prince. The Demon Prince uses different attacks and gains access either to a laser beam or fire orbs, depending on which of the two initial demons he grew out of.

Location
Found in The Dreg Heap. Drop down the pit found at the end of Within the Earthen Peak Ruins.

Phase 1: Demon in Pain and Demon from Below
During Phase 1, the key to surviving is exploiting the difference between the extinguished and ignited states of the two demons. While extinguished, they stay stationary and use two limited-range poison breath attacks, only meleeing the player when close. Outranging an extinguished demon thus renders it harmless. An ignited demon on the other hand will aggressively pursue the player with melee attacks.

This creates two possible recurring situations: Either both demons are burning at the same time, making attacks against them all but impossible and forcing the player to focus on dodging and running away, or only one demon has ignited while the other stays in place and breathes poison, allowing the player to pull the burning demon away from the other to effectively force a much more manageable one-on-one fight. Since a powered demon's attacks come out relatively slowly and do not reach the player when they're standing close to the demon's side, the player can inflict substantial damage to the active demon here until the other demon reignites.

Phase 2: The Demon Prince
The Demon Prince uses different abilities depending on which of the demons from phase 1 was killed last. If Demon from Below (the orange demon) was killed last and becomes the Demon Prince, he uses a long-duration laser ray ability which is easily avoided by staying close to him, allowing the player to inflict free damage while the laser is being fired. If Demon in Pain (the red demon) was killed last, the Prince can throw fire bolt emitting miniature suns in the air and additionaly gains the ability to create a singular large sun above his head. The latter ability can be interrupted by player damage.

It's generally agreed upon that the laser ability is less dangerous because it's easily avoided by staying close. It's thus advisable to kill Demon in Pain first in order to let Demon from Below become the Demon Prince.