As a full time student under my parents healthcare (marketplace) for 7 months in 2024, how can I get the American Opportunity Credit of $1000 without entering form 8962?

If your parents are claiming you as a dependent, you cannot claim the AOTC.  

Also, if you are under 24, and your parents are alive, you cannot claim the refundable portion of the AOTC, only the non-refundable portion if they would not claim you. This means you would have to have a tax liability in order to benefit from the AOTC. 

Thank you for the quick response. My parents are NOT claiming us as dependents this year. We are only listed on their 1095-A because we had coverage through the Marketplace for 7 months out of the year. Aside from that, we are not listed on our parents tax return. We should qualify for the American Opportunity Credit of $1000

You will need to enter the information for your 1095-A on your tax return, but allocate 0% to you and 100% to your parents.  
 
The refundable portion of the AOTC is based on more than whether or not your parents claim you.  If they could claim you, even if they chose not to, you will not qualify.  If you are under age 24 and a full-time student, generally, they can claim you.  You can also claim the credit if you are supporting yourself with income you earn.  

If those items apply in your case, you should indicate this in the interview section for the education expenses and TurboTax will calculate the refundable portion for you.