Dark Souls Remastered | Gwyn boss fight co-op with one phantom on NG+1 - Dark Lord achievement

There are only two endings for Dark Souls and Dark Souls: Remastered and it's rather simple. You either light the bonfire that spawns by Gwyn after his defeat or you don't do so and instead leave the area.

To Link the Fire - Light the bonfire by Gwyn after defeating him
The Dark Lord - Don't light the bonfire and instead leave the area

Gwyn, Lord of Cinder
https://darksouls.fandom.com/wiki/Gwyn,_Lord_of_Cinder

Endings (for Dark Souls and Dark Souls Remastered)
https://darksouls.wiki.fextralife.com/Endings

I do Link the Fire in NG here:
https://youtu.be/8cJOHq8o4X4