The law is written the way it is.  If she is not attending "full time" as the college determines, and she earned more than $4300, she can't be claimed as a dependent.

You don't really file as "independent", you either answer yes or no to a question that asks "Can you be claimed as a dependent by another taxpayer" and this year at least, she answers "no."

For 2020 only, this will make her eligible for $1800 in COVID stimulus tax rebate.  

In general, this means that she will report her 1098-T on her tax return instead of her parent's return.  It will likely mean a smaller AOTC credit, unless her earnings were well over the standard deduction of $12,400, since that credit is not refundable for students under the age of 24.  (It can cancel the tax she owes, so she should get a full refund of any withholding, but the excess can't be added to her refund.)  

If she receives a scholarship that is less than tuition (and reduces the tuition that someone has to pay) that is not taxable and does not change with changing her status.  If she received a scholarship that was more than tuition (covers room and board, for example) then that is always taxable income to the student, and does not change with the change in dependent status. 

Q. Is she ineligible from being claimed as a "dependent" on parents taxes? 

A. Yes. There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.  She cannot be a QC because she is not a full time student over 18.  She cannot be a Qualifying Relative becuse she had more than $4300 of income.  Support, alone, does not determine if someone is a dependent. 

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...

Q. Must she now now file as "independent" from parents?

A. Yes, if she  either needs or wants to file (and she does want to). 

Q. How does that (being "independent" affect tuition paid, AOC, or any partial scholarships she may have earned?

A. Since she cannot be  a dependent and is not full time, she can claim the AOC (including the refundable portion) on her return.  She must either reduce her qualified expenses by the amount of her scholarships or declare some of the schoalship as income if she needs to incease the amount of expenses used for the AOC.