How to attach supporting documentation for Maine State (1040ME) Student Loan Repayment Tax Credit?

You'll need to print and mail your Maine return to include your attachments.  TurboTax doesn't have the capability of adding such attachments to your return.

You'll be able to electronically file your federal return if you want, but you'll need to print and mail your state return.

See the TurboTax Help article How do I print and mail my return in TurboTax Online? for guidance.

As for the best documentation to include, the state doesn't mention any specifics other than what you've quoted above, apparently from the 12 I am claiming the SLRTC for the first time. What information do I need to provide with my tax return? FAQ on the Student Loan Repayment Tax Credit (SLRTC) FAQ page. 

That said, it's often better to include more documentation than less, minimizing the need for correspondence from the revenue office.