The general idea, as usual, is to clone himself several times. Just jump on the real Dreamy Mario, avoid the clones and avoid his attacks well enough that the battle ends quite quickly. Pi'illodium X will retract its wings and turn into a giant hammer. Beware as before Pi'illodium is defeated, it will self-destruct and Mario and Luigi must defeat it in forty seconds. And now for something slightly different! First things first, he might send out a snowball that you have to hammer away.
Dodge the broom for a few turns to avoid this attack. This as mentioned lets you use any attack you want on Bowser Jr without the car blocking it, and generally makes him far easier to hit and more vulnerable to damage. Really, the more you turn, the more you slow down and the more of a chance Bowser has of catching up.
If you time it well, Pi'illodium X will bounce back. Well, he's back, and he's stronger than ever.
Now use the next-highest exit to find 50 Coins and an Ultra Nut , then the next highest for fifty more Coins. Self-Destruct - Presumably unavoidable, at least when you think of it initially. And charge. If you twist Luigi's nose by drawing circles around it, you make wind blow: For the most part, just try to wear him down without getting yourself killed.
So, the two Pi'illos will be released. Collect the eight Red Coins, then hit the!
Bowser Jr can also summon a Bob-omb and have it run rings around the Mario bros. The only way to tell which bro it will hurl it at is after the Eyepi'illo hits either wing. The energy ball attack will now start again.