I can only provide the usual suggestions for it. Don't give up!
* Most of the ring patterns are of two types: immediately near of the current line (when the rings are not aligned with the pipe sides), or exactly on the opposite side (when they are aligned). You should be able to identify them and react accordingly. It's meant to be fast, it's meant to have you miss a lot of rings. The total ring count in a special stage is very high, every section has more than 3x the requested amount so you have a lot of room for error.
* Don't rely on standing on the ground to quickly move on the other side of the screen, jump instead. It will allow you to rapidly land on the other side faster and with better precision than by running.
* Try to not stay in the bottom center. It's the easiest place to kiss a bomb.
* If you need to grab the spiral of rings, tap your controller instead of keeping the button pressed.
* If you light tap when wall running (or on the top part, just like in sonic 2), your character will stay in place for a few moments which will allow you to grab an entire line of rings rather easily.
* If you're in a curve and no rings are coming in the first few moments then there is a circle of bombs coming. Jump!