People like her are way too snobby and must have her head above the clouds.

Quite remember me about my intern boss. She fired a worker, who is more senior than her, just because of personal dispute. The dispute is almost like your case: no respect from boss to subordinate.

Do your coworkers trouble with her too? if so, maybe you all can report her. I don't know about your system, but in my place, if there are so many reports or complaints it will taken more seriously rather than a single report.