She is not eligible, for two reasons: 1. She CAN be claimed as a dependent, whether you actually claim her or not. 2. She is under 24 and does not support herself by working.
There's a new urban myth among college students that says they can get a $1000 from the government just for filing a tax form. For most of them, they simply aren't eligible. A student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit if she supports himself by working. She cannot be supporting yourself on parental support, 529 plans or student loans & grants. She must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit.
She cannot claim a credit if she is, or can be, claimed as a dependent by someone else.
If you are ineligible for the credit, because your income is too high, then nobody can claim the credit.
