From the Super Mario Wiki, the Mario encyclopedia
Hat-to-Hat Combat is the sole story mission of the Cloud Kingdom in Super Mario Odyssey. The mission's objective is to defeat Bowser. The name of the mission is a play on the phrase "hand-to-hand combat."
The mission begins at the Odyssey, and Mario must use the Cap Clouds walk over to the arena, where Bowser awaits. To defeat him, Mario must damage him three times by taking control of his hat and using the boxing gloves attached to it to punch him repeatedly and launch him into the fence surrounding the arena. Once Bowser is defeated, Mario and Cappy are bombarded by cannon fire from the airship. They race for the Odyssey, only for them to be shot down to the Lost Kingdom.
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