I can't complete the challenge "Evade a Spiny Shell by using a Mushroom to boost away from it."

If you successfully evade a Spiny Shell by using a Mushroom, you will see that "Spiny Shell dodged!" is displayed during a race as bonus points gained or after a race on the Actions Performed screen. When this is displayed, it means that you have completed the challenge.
It may take some time to get the hang of it, but you can do it!