How can I prepare for my NEET exams in parallel with the boards?

Considering the syllabus of NEET, for a CBSE student preparing for both the exams (boards and NEET UG) should be an easier as compared to state boards students.

If you are Preparing for 10+2 boards from any state board or CBSE board that means you are preparing for both 12 std board exam and NEET. The syllabus of 12th Board exam (especially CBSE) is included in NEET syllabus.
In biology be thorough with NCERT. For chemistry and physics first cover the complete NCERT and  you will have to work a little extra using some additional books. (https://www.schoolmykids.com/college-admission/best-books-to-refer-cbse-neet-ug-entrance-exam/)