Cougar Attacks United States and Canada.
Mountain Lion Attacks from 2001 to 2010
Lots of good information. People who are attacked are usually unarmed and do the best they can.
Mountain Lions (cougars) normally bite down on the back of head or neck and do not let go. They try to bite (puncture) neck or head. They try to shake to break neck and try to cut neck with claws. Typically if hiking with a friend that friend beats on it with logs or rocks until it lets go and runs. Anyone armed with anything has less injuries than otherwise.
It is one of many cases where range or accuracy is no big deal. One older lady tried to push a ball point pen in the mountain lions eye while it was biting down on her husbands head. She had no luck pushing the pen into its eye so eventually beat it off with an old branch until it let go and ran.