I was covered in parent's health insurance through Marketplace (august - december). They're not reporting me on their taxes. Do i need report 1095-A?

Yes, you will need to report your share on the 1095A. You will need to get a copy of your parent's 1095A and report it on your return. After you report the 1095A, there will be a follow-up screen asking who the taxpayer is you are sharing the policy with and what percentage of the policy amounts you would like to claim on your return.