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?
This is indeed an odd sentence, but she might be a sportswoman. That's actually what came to my mind first.
This statement could well be made about a female celebrity. What I found odd is the word order, which I had to look at for several minutes before I could figure it out.
is it wrong? should it?
she is very succesful thanks to her body that she takes good care of
that replace with which