This was done on Gear 2 (Normal Difficulty)
I may or may not have forgotten about my mouse in a few of these runs

Also, as of version 2.2, Sneaker Cups and Barrier Cups special stages have been swapped.

Time stamps:

0:00 Ring Cup

1:19 Sneaker Cup

2:41 Spring Cup

4:26 Barrier Cup

5:53 Invincible Cup

7:17 Emerald Cup

8:40 Extra Cup

10:14 S.P.B Cup

12:08 Rocket Cup

13:34 Aqua Cup

15:13 Lightning Cup

16:40 Flame Cup

18:40 Super Cup

20:32 Egg Cup