Bullying bosses are a very real and very troublesome problem in many workplaces.
Unfortunately, most of the discussion that I've seen of bullying bosses doesn't offer any solutions that get at the root cause of what's going on. This article gives three options: (1) ignore the boss (2) confront the boss (3) go over the boss's head. I think none of these are the best issue. Ignoring it doesn't solve anything, confronting the boss directly might make things worse, and going over their head could also backfire.
Is there another way out? I think there is. I think that I would recommend (a) finding ways to insulate your own well-being from the negativity of the boss, maintaining an inner calm (this is a useful skill for anyone to learn, so you might as well see the boss as a challenge, an opportunity to grow in a key way that will yield benefits for years to come) (b) finding ways to approach the bully with compassion, in order to undercut the root cause of the bullying (which is usually a sense of powerlessness in the mind of the bully, which he or she tries to regain in non-constructive ways). Some bullies can be overcome by flooding them with positivity and by drawing out positive qualities in them. (c) thinking critically about the institutional culture in your workplace: Why is the bullying going on? Is your boss responding to a system of incentives that creates stress which he or she passes on to you? And why is the boss allowed to bully without being reprimanded or guided to be more positive? Is the situation fixable, or should you start looking for another job?
I ultimately think this is more constructive!