Homing attack the pulley and light speed dash on the first dash ring and stomp into the red ring.
You can either magdash off the pulley, as done in the example run, but you can just boost into the rainbow rings instead by holding right and boosting.
Get into the dash ring that brings you up to the red ring.
Land on the yellow box with the 10 ring on it, boost jump off of it and homing attack the pulley and light speed dash the red ring.
Homing attack the pulley and the spring.
After you light speed dash the red ring above the dash ring, hold up right-ish and boost to land on the button and then homing attack the pulley.