Follow the path, defeating the goons as you go. Head up the stairs and you'll find yourself in the Shaded Woods.

On the second floor are more goons but they'll stay in their rooms if you leave them alone. In the next room you'll find a bonfire in the door to the left and a chest in the door to the right. This will just leave the basilisk to deal with when the gate opens. After one of the doors is destroyed, if you position yourself right, you can shoot a goon in the head and lure them all down, without having to trap yourself in. Note* If you find yourself having trouble dealing with the goons, try aiming with a bow and destroying one of the doors at the top level.