If you are always dying while fighting an animal, there is a way to avoid dying entirely. In fact, you can avoid getting any damage at all.

When in fighting mode, continuously click the right (or left, whatever is your preference) button. Just keep on pressing it. The animal will lounge at you but will miss because you keep on step-siding to the right (or left -- just go in one direction constantly).

When the animal starts to go back into its resting position, hit the animal. Repeat this as many times as it takes to kill the animal. Using this exploit, you can kill an animal easily with just your fists (which, of course, would take longer than a weapon)!