She is ineligible for the tuition credit.
A full time unmarried student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working (earned income). She cannot be supporting herself on parental support, 529 plans or student loans & grants. She usually must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit.
There is a provision to allow the parent to forgo the student's dependency (and the $500 credit) to allow the student to claim the NON-refundable portion of the credit. But, since your student has no tax liability, that doesn't work for you.
