Okay, I watched this anime a long time ago. I was litte so it was about over ten years ago. Because of this I remember very little about it but I am going crazy trying to find it.

Alright so, there was this kid with a sword and I remember there was a talking tiger or at least something that looked like a tiger. The only episode I really remember had the guy and a girl at the edge of a bottomless pit. There were two ropes hanging over the pit. One would make them fall to their deaths and the other would allow them to pass safely.
The girl sacrifices herself by jumping to one of the ropes. It ends up being the wrong one and she falls. The guy gives her the hilt of his sword to hold onto but can't pull her up because he's holding the blade and cutting his hands.

He refuses to let go but the girl, knowing he can't pull her up, lets go of the hilt and falls into the pit.

Later the guy's fighting some evil overlord or something and there's lava all around them.

Does any of this seem familiar to any of you? That's all I can really remember.