I need advice...

I need some advice. I was hired as a director of nursing. I have been working there for almost a year. I am making good money; however, the conditions are almost unbearable. The head of the company is a major bully. She feels the need to belittle me, in a crowd, whenever she sees the opportunity. She is really mean and unprofessional. My immediate supervisor does nothing to shield me from these attacks, and does not appear to speak up on my behalf. I know that I have made many improvements in the company (higher standards, infection control, quality of care improvement, morale boosting, etc., etc., etc.); however, according to the lead, I have been doing nothing. I really would like to stay at this company, because I can see the potential in my staff and this position qualifies me to receive student loan repayment from the government.

I know that many of you will respond that I should talk to the the lead; however, this will not fly with her. If I do, I will most assuredly be put on the "let's find a reason to fire her" list, according to the history that has been shared with me by numerous other employees. She is not the type of person that can be reasoned with.