How do I report advance American Opportunity Credit that I received in October 2021 for $1500?

There is no advance American Opportunity Credit. You will have to clarify who sent you $1,500 in October, and why. With no information other than the amount, there is no point in our trying to guess what kind of payment you received.

Also clarify whether the amount was exactly $1,500.00.

It is called American Rescue Plan-FA Refund in the amount of $1500. Do I need to report this an income on the tax return? If so, in what section?

Thank you for help.

That is not taxable or even reportable. 

See https://www.irs.gov/newsroom/emergency-aid-granted-to-students-due-to-covid-is-not-taxable