"She is responsible with her studies."
Translation:Ela é responsável com seus estudos.
If you substitute "money" for "studies" does the sentence make more sense? If so, perhaps that will help orientate your viewpoint when you go back to the original sentence. It basically means she studies in a responsible manner.
I've just found a nice quote that contrasts "for" and "with": "If she is responsible for your smile, be responsible with her heart."