If I am covered under my parents' Marketplace Plan do I need to include any Form 1095-A info on my individual tax return? I am a full-time student who works part-time.

It depends.  If you are full time student, are your parents claiming you as a dependent?  If they are, then you do not need to enter this on your return.

If you are not being claimed as a dependent, then yes, you will need to enter their 1095-A on  your return.  Then you will need to allocate the premiums.  Many times parents who pay the entire bill will claim 100% and the child claims 0%.  You can agree to any number as long as it adds up to 100%.