I want to call Ruth Bader Ginsburg a badass, and I am worried this won’t go over well.
If you have to ask, then the answer should be no.
I would avoid it and choose something more professional/academic sounding.
Never, ever, in formal writing call a Supreme Court Justice a badass, even if she is. She might be tenacious, persistent, or resolute but never a badass.
Certainly you can find another word…
She is a badass and probably revels in the term herself. You could settle for The Notorious R.B.G. but I’m not joining the above nay votes.
You could refer to her as notorious. 
Hmmm, I might be a dissenter but I think you can get away with it, depending on the rest of the essay, your writing style, etc… But be careful, this could backfire.
I like your answer @AboutTheSame 
@Lindagaf (and others): if you have a spare hour, I recommend this video.
https://www.youtube.com/watch?v=ctYY6RivjEQ
Personally I don’t think of that as a curseword, and I am likely showing my age (33). I was expecting something far worse from your title! So it depends: at many institutions, the person reading your essay may very well be about 25-30ish and not bat an eyelash. Or you may get a veteran, who is older and may well. So it’s up to you–a calculated risk but I don’t think a dealbreaker with every reader.
I agree with you that it’s not really swearing, @proudterrier, and I’m 64 – but dad was a Marine, so I always figure my scale may not be normal.
Badass is completely fine in a college app essay. As I posted somewhere recently, I’ve even seen F-bombs in successful app essays (I wouldn’t recommend that though!).
RBG is a badass, and I wouldn’t hesitate to say so in an appropriate way.
Depends on the school but it’s probably fine. Stuff like that lets them know you and that’s what they want. My kids didn’t curse but they definitely did use teen language, song lyrics, movie references, etc that was true to who they really were. Both accepted to top schools.
Badass? Rogue, reprobate, recreant, maybe apostate. Badass sounds like comic book villain.
@TooOld4School - The thing is, none of your terms describes RBG as well as the OP’s.
I’m a mom of college age kids and I have no problem with the term. I’d call it slang more than swearing.
@sherpa, that is a matter of opinion, which I would love to expand on, but the mods don’t allow political talk.
“Stuff like that lets them know you” Yeah, but is it what you want them to “know?” The rest of the writing- and the thinking, from the first few words on- is going to need to be spot on.
It’s not whether we like or mind the word. It’s what OP ends up showing about his thinking (judgment and ability to self edit, not what he “thinks” of RBG.) He’s talking of Northwestern, not a hs essay. Not a note to a teacher who knows him and has the perspective. So think about it.
She is a badass… but she can be described with a lot of other adjectives, too. Just like we don’t advise that students use certain topics for their essays because surely there is more to their lives than the inappropriate thing on their mind, you also likely have a large enough vocabulary to get beyond badass for RBG.