From the Super Mario Wiki
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When using this item, Luigi puts a gold shell with a trampoline on his head. Mario jumps on the springboard, and the player must control Luigi with to allow Mario to land on the trampoline each time he comes back down. If the player presses at this moment, it will let Mario fly higher. After the brothers get close enough to the enemies, Mario lands on the selected baddie ( button command), although if Mario misses the trampoline, he will fall to the ground and the attack will end without dealing any damage. The attack will be stronger depending on how many times Mario successfully landed on trampoline (with the command), as well as how well Luigi lined up with his brother each time. The best result has Mario jumping higher than the screen for the final jump, while somersaulting for every jump. It cost six SP to use this attack (three if reduced). In order to use it, the Player must collect all 10 Flab Zone Attack Pieces.
The Juuuuuump Mode in the Challenge Node is solely focused on the Jump Helmet. Making Mario jump to the right of the helmet makes him jump farther and making him jump to the left makes him jump higher.
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