Don't ask your professor to curve if he has stated from the first day of class that he will not do so. His classes may have the reputation of being difficult to pass, but it is important to not try to convince him if he has already said he won't. You run the risk of him grading your work more harshly and having a negative opinion of you.
Find out how many students in the class have failed or are about to. Avoid appearing as if you are trying to gather the information to gang up on the professor or that you despise her and want to get the whole class behind your effort to show her she is a bad teacher. You do, however, want to be sure that the rest of the class has done as poorly as you and that your grade isn't just one of the few bad ones before you ask for a curve.
Approach the professor during office hours or ask for an appointment. Office hours are the best time to discuss such a problem as the class needing a curve to pass. You will have more time to rationally discuss the situation than if you try to catch the professor before or after class. You can lay out your arguments for the curve better when you have time to talk about them, too.
Study the professor before you speak with her. Know about what she likes and doesn't like, what her goals are for the class and what makes her mad or happy. Take time to tailor your arguments for a curve to suit her individual personality. You might emphasize that many students attended tutoring on a regular basis, but did not find the tutors effective. Therefore, their grades did not improve.
Use any evidence you have gathered from other students about their experiences studying for and passing the class. You might include an opinion from one or two of the students supporting your request for a curve.
Ask for extra work or a test make-up if the teacher does not agree to a curve. This demonstrates that you are willing to work to do well in the class. Your professor's estimation of you will likely increase when you ask to do work instead of asking for a curve.
Speak courteously and respectfully to the professor during your conversation. Avoid badmouthing him when you get out of the meeting if he does not grant your curve. Continue to work and study hard in the class to silently demonstrate that you are willing to do what it takes to get the job done.