1) On the first staircase you grind on (before the rainbow ring).
2) Look for the fountain in the big open area and jump on the spring where you'll find balloons. Follow the balloon trail through a path to a 1 Up. Stay on high ground and you'll see boosters and a small tunnel with a red ring in it.
3) After hitting a checkpoint and going to the 2D perspective, you'll find some panels that you have to wall jump onto. You'll find your Red Ring here.
4) From 3, follow the upper path, and you'll be thrown into a bumper and spring poles. Use the homing attack up the balloons you come across and follow the path to get the red ring.
5) It's in the long stretch of road where you have to quickstep and avoid the enemies' lasers. Keep to your right, and it's on the right-hand side after the first turn. It's in this
video (I know it has terrible audio sync problems, but it's the only video I could find. This player gets the ring at 6:56.)