Q. If I am still claimed by my parents on their tax return do I get to claim the Tuition Tax Credit?
A. No. The tuition credit goes with the student's dependency.
"It makes a huge difference in my taxes".
That's unusual and is most likely due to an entry error. College age students are seldom eligible for the credit.
That said, if this is a case where your parents aren't eligible for the credit (their income is too high), there is a way for you to claim the credit.
While technically there is a provision that allows a student-dependent to claim a federal tuition credit, from a practical matter it seldom works out. A full time student, under age 24, is only eligible for the refundable portion of the American Opportunity Credit (AOTC) if he/she supports himself by working. She cannot be supporting herself on student loans & grants and 529 plans and parental support. It is usually best if the parent claims that credit.
If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit. The student must still indicate that he can be claimed as a dependent, on his return. This is worth up to $2500 (AOTC shifts to all non refundable)
