The End of Fire
To get this ending, you have to access the Untended Graves optional area. After defeating Champion Gundyr, head to dark Firelink Shrine and look for the Eyes of a Firekeeper key item. You’ll find it behind an illusory wall at the end of the corridor on the bottom floor. Roll through the wall, pick up the Eyes, and head back to Firelink Shrine to give them to the Firekeeper. This will cause the background music in Firelink Shrine to change.
After defeating the Soul of Cinder, do not interact with the bonfire. Instead, look to the left of the bonfire and you should find a summon sign for the Firekeeper herself. Summon her, and the ending cutscene will be triggered.
There is also an alternative version of this ending. After the cutscene, as the screen starts fading to black, you’ll have a few seconds to attack the Firekeeper and kill her. If you do this, you’ll get a slightly different version of the End of Fire ending.