There are three goals in this stage, a blue goal, a green goal, and a red goal.
To get to the blue goal, go to the right or to the left on the first ring. If you go to the left, you will have to roll directly into the goal. Whichever way you take, make sure to have enough momentum to stay on the ring. Jump off onto the second ring with not too much momentum because you will bounce over the goal or slide off the ring but not too slowly because you will not make it period.
Keep jumping off the rings until you are on the fifth ring. Make sure you jump where the jump marks are located as they will help guide you to where you should jump. Once you are on the ring with the goal, roll into it.
Repeat the same pattern as the green goal strategy, except jump until you are on the eight and final ring. Once you are there, roll into the goal.
At the beginning of the stage, on the starting platform, if you tilt to the right of the platform and stay at the right, going forward with a little adjustment, you will be able to get into the red goal without serial jumping as you would normally.