The downwards spiral is something you'll see again and again as a CFI. The person, not gender specific, makes a mistake, gets mad at themselves, makes more mistakes, gets more mad, and the spiral continues.
Break the spiral. If you can't laugh it off or teach the student to laugh it off, then end the lesson when the person gets too hard on themselves. There's an extremely important lesson the student needs to learn and it is only remotely connected to flying. It may take only a few lessons before the student starts calming down and moves beyond the mistakes. It may take more. Explain that ending the lesson is not punishment, it is simply habit reformation. This student has a habit of self-castigation that needs to be broken and reformed into something more productive to flying.
Make it into a game. Say she only gets 10 "sorries" in a lesson. Count 'em. "That's one.. nine left...." Make light of the situation. Take it to the extreme, make it so silly they have to laugh. Exaggerate cupping your hand over your headset's ear cup, "did I hear a soorrryyy coming out? Aw, blast this noise cancellation, I thought you'd almost apologized again." Or directly confront it, "you'll never get me to believe that" in response to "I'm an idiot" or similar. When the outcry is "I'll never get this" or something expressing the frustration of having tried something only done 100 times before, respond "you can't have it perfect now."
Praise the student's courage for going out and displaying all of his or her imperfections to an audience. Explain that if one is not scared, one doesn't need courage to go out and do this. Let them know constantly that as long as they keep showing up for lessons, making mistakes, going home and blowing it off, then coming back for the next lesson, they will succeed, after all, you're their instructor.
Absolutely do NOT criticize the person. Sandwich the things to work on between the praise of the person. And the things to work on are "when we do this" or "it will work better if we try this..."
Set the bar lower. "Today we're going to scare the runway, working on our go-arounds, the float, and the flare." You control the power, they control everything else including trim. You guide them down to 10 feet above the runway, then 5', then 2', working ever so slowly down. Work on crosswind correction, fly over the centerline, then the left TDZ marker, then the centerline, then the right TDZ markings. Eventually have them work the power, their controlling height, position, attitude based on your directions. Depending on how the lesson proceeds, during one of the low passes, reduce the power enough so that they actually touch down. End the lesson at that point, "That was a great landing (touched on mains going mostly down the runway), we're stopping on that. You can have no arguments on that, it was a great landing." Then go on to the lesson debrief (in private!) asking "what did you learn" and have the student tell you.
For another lesson, write down everything the student did right. It will change your mentality too. Your writing stuff down will definitely increase their nervousness level, but they'll be shocked when you show them your kneeboard with all of the positives at the end of the lesson.
And never let on that you've never dealt with a student like this before. Share some stories of other screwups, even if you have to borrow some of mine, like the fellow that took 5 tries to pass his IFR checkride (now flies a Hawker and is doing just fine), or the fellow that needed over 300 hours before he was comfortable flying a high performance hot rod and ready to take his PPSEL checkride. Whenever the "how long to solo" or "I haven't soloed yet" gripes come up, remind 'em that this ain't a farmer's field in Kansas, it's going to take more than 10 hours of flight time to deal with everything that comes with modern aviation, then list them. Students will perform to your expectations.
Let us know how it goes.