You need to light four bonfires to enter the dungeon in this area. Go to the right side of this location where you must fight a few enemies guarding the fire. Take them down and mark three bonfires, one will be to the right of your screen hanging over the abyss and the rest is to your left and front. Hit all three objects with your Vorpal Blade but hit the lit one first, it is hanging in the air. Once these three are lit the main bonfire will lit itself.
Now go to the left side of the main puzzle area where the bonfires are, mark the two bonfires there and the main bonfire will lit itself. Light the final bonfire to enter the dungeon.