Could you possibly convince her that being successful, in this particular situation, might not be about getting an A or being "perfect" but about staying true to herself and keeping her own voice in the face of unrealistic criticism by an authority figure? Sort of reframe the situation for her? From what you've written, it seems that there is very little value in "achieving" what he is looking for so why even try? What is the benefit to her other than the grade? It actually sounds like achieving this goal would actually be a loss.
I realize it undermines his authority as a teacher, but I sort of think he deserves it. In a situation like this, I would argue that keeping your own voice and perspective is actually much more valuable than the A. The A is arbitrary and unimportant in the larger scheme of things. Try to convince her that being "perfect" in this situation means taking a B, but knowing that she stayed "perfectly" true to who she is and what she knows to be true.
Because at this point, it sounds like there is very little likelihood of significantly changing his perspective, so perhaps you can focus on helping her survive the situation with her nerves and psyche intact.
