How can I let my friend know that she's not ugly?

So I was on the webcam with a friend earlier and out of nowhere she calls herself a fat cow. I tell her that she doesn’t. that she looks great because I honestly believe that she does. But then she goes on to say that I have my opinion and she has hers and that I can’t change her mind, and she’s not going to let me. So I have to deal with that and I said that I’m not going to, and like I keep saying I never have. I just don’t want her to feel down so much. She says that complimenting her and saying she isn’t ugly doesn’t help.

So what am I supposed to do? I don’t want to make another mistake and have her feel even worse. I want to help her realize that she is indeed a beautiful person. From the bottom of my heart, what I see when I see her is a beautiful person, but she doesn’t see that, and I understand that it may be hard for her with what she’s gone through and the way people has treated her regarding her appearance. I just despise the fact of feeling so helpless to help her.

Even if I can’t convince her 100%, how can I at least get her to feel a bit more better about herself? I know I can’t make her, but I have to try.