From the Super Mario Wiki
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A Double Kick is an attack that can be done in Super Mario Galaxy and its sequel, Super Mario Galaxy 2. It can be used to defeat many enemies and to use certain items. To accomplish this, Mario must run toward an enemy and Spin when he gets close to the enemy. Then, near the end of his Spin, Mario must perform a Long Jump by crouching quickly and jumping. Mario does a Long Jump, but he has a few sparkles around him, and he is able to defeat most enemies that are in his way. This attack does damage only when Mario is rising; when Mario is in his falling animation, the Double Kick turns into a regular Long Jump and has no damaging effect. However, Mario can Spin when he is falling to protect himself from getting hurt.
Mario must time the attack correctly for it to work. If he Long Jumps at the beginning of the spin, he does a Spin Jump. If he Long Jumps too late, he does a Long Jump. This move can defeat certain enemies and can also break Crystals and activate Chance Cubes, Lever Switches, and Gravity Arrows. However, it cannot break some Crates. This move is called the "Double Kick" because of how Mario lifts his legs when he performs a Long Jump, resembling a kick with both legs.