I gently disagree with the above poster. One of our jobs in nursing is being an advocate for our patients. This classmate is not a patient, but she clearly needs an advocate. Many times people who are in this situation feel that they deserve this treatment, and feel helpless to do anything about it.
In most situations, it's proper to talk to the instructor first about an issue before going over their head. If you have reason to fear reprisal, however, then I would say to go directly to the administration.
I would draft a letter in a clear and professional manner (spellcheck is everyone's friend!) stating, in this order:
Intro: Issue/s with the instructor, and why you are not going to her directly but are rather going right to administration.
Body: Here is where you detail the issue/s, giving concrete examples. Name the student, cite specific examples, and keep emotion out of it. You can state how you feel this student is being singled out, but back it up with facts. Try to avoid terms like, "Picked on" or "mean" of "disgusted", instead use terms like, "inappropriate and negative facial expressions, eye rolling", "behavior bordering on verbal abuse, directed only at this student", and "different expectations for this student than for any other". You can also state that the student in question is unaware of your letter--and I would KEEP her unaware, honestly, until you've sent it.
Summary--make it short and sweet, but sum up your issue and state what you would like to see happen. Don't say that you want to see this instructor fired--be constructive in your goals. You would like to see more professional behavior on the part of the instructor, and to see all students treated fairly and equally, yadda yadda. State how you are available to explain and/or discuss this further, if the administration has any questions.
If there are others in your class who you trust and who would be willing to sign this letter, get them to sign and then take it to the Dean of Nursing, as well as the advisers. An anonymous letter will be given very little weight, but a signed letter shows that you are serious about this.
I'd also encourage your classmate, without talking about this letter, to go to talk to the instructor, and see if she can work this out. Sometimes just going to the instructor and saying, "I seem to have difficulty doing what you are looking for, and no one else does. What can I do to improve? What can you tell me that I need to work on?" If the woman's a total hater, she's not going to be constructive, but it's a step that this student needs to take before she goes to the dean about this issue. If she does go to the dean, your letter is there, corroborating her story.