clinging to walls.
I killed him on my fourth attempt. The first time I died was due to pure ignorance. The second time I was too brave and tried to go toe to toe with him, there just wasn't enough space to roll away from his blows. Dead. The third time I got stomped on. The fourth time, I killed the archers on the top, and used the tower to deliver my first blow on the Taurus Demon from on high. I did it twice more -- and when he managed to jump on the tower where I would be, I would stay on the ladder by the wall going up to it. I notice that he couldn't see me and jumped up and down the tower top looking about for me. I lopped a couple of fire bombs and stabbed him from on high again and he was dead. It was still a close fight.
There was no encounters after that until I reached a bridge. As I was crossing it, a red dragon swooped in on high and singed me to half health with its breath of fire. And now it's crouching on the other side, breathing steam. Backtracked to the last bonfire to recuperate.