How do you unlock the C-Sides?
You have to beat all B-Sides to unlock the C-Sides.
To get the B-Side version of the Core, you will need to collect all 8 crystal hearts from the normal versions and the 7 red crystal hearts from the first 7 B-Sides. Once you finished the final B-Side level, C-Sides will unlock. To play the Core C-Side, you also need to beat the other 7 C-Sides first.