This is story-related and can't be missed.
Acquiring the Lordvessel is your main objective in the game after you have rung both bells and it is done by pushing your way through all of the city of Anor Londo and beating the boss pair inside the largest building: Ornstein and Smough. Once you have done that, progress to the next room and you'll find Gwynevere, the Princess of Sunlight. Talking to her will grant you the Lordvessel and the trophy.
You can still acquire the Lordvessel if you kill her but be warned that the entire Anor Londo area will become dark and all enemies of the level (except for the painting guards) will be gone and only two humanoid enemies will show up in the main hall of the main building. By doing this you will also not be able to join the Princess's Guard and Blade of the Darkmoon covenants in this playthrough.
Once you acquire the Lordvessel you’ll be able to warp from any bonfire to select major bonfires around the world instantly.