What to do when your boss wants you fired?

A friend has been having a really tough time at the company he works for. He had a good start, quickly moved up and is getting paid very good. For some reason his boss who is like hitler reincarnated looks for anything to give him write ups. i e....last time he said a little comment which was supposed to be funny and she used it to her advantage to say he was mocking the company, which he then had to deliver a speech on why he should keep his job! Then they get after him for throwing 6 papers away and not throwing them in the recycle bin. No one else in his department gets reamed out for things like this and the other people are much more vulgar and wasteful and theyre all useless!!! What can he do? The company he works for is pretty big and its a call center. Cant he say something to HR and they should address this ***** to correct herself?