Let me start off by saying that there are way too many stories of cowardly men beating up women. That said, here are some true stories of women winning against men.
I'll start with the case of a very big woman being held up at gunpoint by a teenager in a project where I used to work. I got all the police reports for my tenants. In this case, a teenager pulled a gun on a woman on the street. There was a garbage can out on the street. She picked it up and busted it over his head and he ran away, gun and all.
I worked with a girl who was tall but skinny, and was assaulted by a group of young boys in a parking lot. She threw them off her back like insects and they took off.
A skinny girl took ONE martial arts lesson. It wasn't a karate class. It was a class where the lesson that day happened to be about finger locks. Leaving that class, she was assaulted by a man twice her size. She grabbed his finger, twisted it as she was taught to do a half hour earlier, and he sank to his knees and gave up. When she let his finger go, he didn't continue the assault. He was more than done.
A Tony Blauer story. There was a mother and her teenage girl off in the woods of Canada somewhere, out in the middle of nowhere. A man busted into their cabin holding an axe. The first thing he did was use the axe on the mother, striking her high on the arm. She fell back onto her bed with a broken arm and should have gone into shock. The teenage daughter jumped on the man's back to prevent him from finishing her mother off with the axe. The man didn't hit the girl with the axe but shoved her across the room where she fell. He took a few steps towards the young girl, holding his axe high. The mother then got up and attacked the man like a lunatic, with no weapons at all, and he ran out of there and was never heard from again. Tony ironically said to the woman, "Where did you get your black belt?" His point was that when you are protecting a loved one, you suddenly fight as if you are a black belt.
Another Tony Blauer story. A woman held a tupperware party in her home and had all her girlfriends over. During the party she got tired and went to sleep, leaving her girlfriends to enjoy themselves. When she woke up there were only three people in the house, and she was one of them. The second was her sleeping young baby. The third was the boyfriend of one of her friends. He raped her and beat her up in the living room. She cowered like an embryo. He raped her and beat her up some more. She begged for her life, terrified. Then he went into the kitchen and brought out a collection of knives. He said "Now we're going to have some real fun, wake up your kid and bring her downstairs." The woman went berserk and attacked the guy she had been cowering in front of, and he fled the house.
One last story. One day I decided to teach my mom a simple way to trip someone who is bothering you. We had a lot of fun with it, flipping each other backwards and landing on the couch. Very soon after that, she was standing on a New York City subway platform, all 5 foot 2 of her, and a tall young man stood next to her and put his hand on her purse. He waited in that position for the train to come. When it came, he snatched the purse. As he tried to run with it, my mom tripped him and he landed so hard that he cracked his head on the subway pavement and was out cold. My mom reached over his inert body, took her purse back, then had to step over his body to enter the train.
I made the point on another post that a light girl can prevail over a football player with certain martial arts moves, notably the extended arm bar called juji gatame, and the rear naked choke, and various finger and joint locks. There are ways to position yourself so you have many times more leverage than the strongest man ever could, applied to a sensitive target. As an example, I could take a 90 pound 12 year old girl and position her body and her arms in such a way on a man that he wouldn't have a chance against her once he was caught in that position. She'd either break something on him or kill him. When you think about it, that is the sole purpose of all the martial arts. It is unnecessary to develop a martial art that teaches a big bruiser how to kick the shit out of a weakling. It's the other way around - that's the raison d'etre of the arts. If a martial art can't do that, it isn't worth much.
With that in mind, don't get the idea that a black belt in karate can make a woman able to out-punch and out-kick a big tough guy. Women shouldn't be planning on a boxing or kicking or karate match with someone twice their size. They need better techniques than that to even the score. Punching and kicking give way too much advantage to the big guy. They just hit so much harder, regardless of technique. The way for a woman to beat a strong man is either with submission holds or by just going ape, freaking out, and attacking like a wild banshee with nails to the eyes, and teeth on the throat.