This is a very odd sentence. Does it mean she is successful because of her body? I can't imagine anyone ever saying this.
Yes, that is the meaning. And I don't have a problem to imagine this sentence in a tabloid when talking about an actress.
I don't know what's odd about it. There are many "professions" where looks are one's most important attribute, and they are a big advantage in many others as well. Never heard of models?
I can imagine many sexist people saying this. Is this necessary to learn in a language course? I rather think not.
Wonder where is the male version of this (he is only successful because of his body).
She can be a fitness coach for example :)
This is indeed an odd sentence, but she might be a sportswoman. That's actually what came to my mind first.