Use custom equipment to boost his attack so he can break the harder blocks faster, but remember it cuts your defense too, so you have to seriously watch out for the bomb boxes. And make sure to at least have one of those be an equip that gives you a beam sword. This greatly increases your range, and ability to knock away the bomb boxes without danger.
Oh, and when the fever meter is about to run out, let some of the red blocks build up on the stage so when it ends, you can hit them all at once. It'll get your meter back up half way almost instantly.
I just finished the challenge about a day ago, so all of this was fresh on my mind anyway lol