I was that girl once - I was 14 and hated PE. I absolutely HATED it. I was a late-bloomer, and I didn't start puberty until 13, and I was embarrassed about my body. Also my hips changed shape and it took a while to get used to them; I grew really tall and I fell down a lot, and was just generally quite awkward. I had very little athletic endurance. I couldn't run for more than 10 minutes without serious pain, stitches in my side, out of breath. Now I'm a grown woman who hikes every weekend and has walked across the Alps. I hope that sharing how I got from the girl I was then to the athletic woman I am now will help you and your daughter.
My parents helped me with the short-term problem - we talked to the vice principal and found a way for me to meet my gym credit requirements through a correspondence course (I imagine today it could be an online course, but such a thing didn't exist back then). I had to do swimming 3x per week on my own and have the lifeguard sign a record of the time I spent. I did another course the next year for aerobics, again on my own, at home. I loved that it was in private, so no one saw if I happened to make a fool of myself while trying. And as a bonus I was able to spend the time in school doing studio art instead of gym, which I really loved. I knew I only got to do that if I successfully completed my gym requirements outside of school, which was an extra motivating factor.
In the long term, I slowly got used to my body, and built up my endurance. My parents didn't do much to help me with this, the gym correspondence courses did help a bit, but it was mostly just self motivated. I wish my parents had taken me out running/hiking/playing sports more, but they weren't that athletic themselves, and neither were my friends. Exercise gets so much easier and less painful if you do it regularly, it just takes a bit to get over that hump.