Layal,
In regards to the latest version of your logline, there is a 'first principle' about loglines deriving from the fact that movies are first and foremost a visual medium.? Therefore, every element of a logline should refer to a specific person, place, object or activity that can be visualized on a movie screen.
For example, if the script is about a? character's struggle to win Olympic gold then the visual (and audio) that informs the audience that she has succeeded is standing on the highest step as the Olympic gold medal is placed around her neck and the national anthem is played.
So what's the visual for "prove herself"?? ? What will that moment look like on a movie screen?? What will it sound like?
Unfortunately, not only does? "proving herself" seem vague and undefined in terms of a specific visual moment or prop, I suggest it also seems to be more of a subjective goal than an objective goal.? Of course, a script is all the better for having a secondary subjective story line,? but loglines are only about the "A" story, the pursuit of objective goals, not subjective ones.
(And who forces her to take the miserable job?? You need to be specific.)