Ill-advisedly is the adverb that matches ill-advised. You use it when you want to say how someone did something: they acted in a way that was not wise, and trouble was likely. It sounds even more formal than ill-advised, so you will meet it in careful writing more than in chat. Many teachers would rather recast the sentence (“It was ill-advised of her to…”) because the -ly form is a mouthful. Though actually, if you need the adverb, this is the real one — English does not let you say “He spoke ill-advised” and call it finished. Same meaning as the adjective, just sitting on the verb.