From the Super Mario Wiki
When Mario must reveal who murdered Mayor Penguin, he'll come across a locked door. Eventually, he'll also stumble across a key trapped underneath Shiver City's frozen pond. To break the ice, Mario must Tornado Jump on the lake the times, or blow it up with Bombette. If Mario tries to break the ice before visiting Mayor Penguin, his actions will be disapproved of by the penguin patrol and he will be thrown off the premises, to the area west of the pond. Once the ice is shattered, Mario can dive down the key with Sushie to claim it.
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