Illegal harassment? Based upon what theory? Age, sex, race, gender, pregnancy, disability? Harassment of an employee on the basis of a protected characteristic is a violation of anti-discrimination statutes. Is the behavior sufficiently severe or pervasive for a reasonable person to believe that the conditions of employment are altered and the work environment is hostile? Is the work environment uncomfortable? Sure is. Have the conditions of employment altered? Really not enough information, but doesn't appear so. Is the work environment hostile? I don't know. Does this person treat everyone the same, equally demanding? If so then it's not based upon any protected class. A boss can be ignorant, rude, demanding, crude or vulgar, providing all employees are so treated. Leona Helmsley (God rest her soul) was a demanding boss, however she was not guilty of harassment, just not paying taxes.
As to HR, it has been my experience that it views its job as protecting the company, not in policing employee relations. Unless the harassment/hostile work environment qualifies as a violation of law, most do not want to get involved. No, it is not their job to make sure the employees get along, it is their job to protect the company, which is the same responsibility of all employees. They are not "Super Nanny" and do not get involved in teaching people proper methods of interaction. If this boss has someone she looks up to, then approach that person, as it is easier to accept correction from someone whom you look up to.