。
She really wants to lose weight.
Literal
She [topic-は] very lose-weight-want-show is.
~たがる is the third-person 'want to' — Japanese is careful not to put words into other people's heads, so claims about someone else's desires use this 'shows signs of wanting' suffix rather than the bare ~たい reserved for first person. The ~ている form here pictures her wanting it as an ongoing, observable state. 痩せる ('to become thin') is the standard verb for losing weight, though ダイエット (loanword 'diet') is just as common in casual speech.