From the Super Mario Wiki
Toad's Vest is an item found in Paper Mario: Color Splash.
It is one of four items Mario must retrieve for Justice Toad in Cherry Lake. East from Justice Toad's hiding place, southeast and further along south is an area with a water-wheel which is not operational as a blue Slurp Guy is draining the stream of its color without stop. After Mario manages to navigate the docks and get to the Blue Slurp Guy and defeat him, the stream will flow and from there, Mario is able to reach the Toad's Vest by jumping down from the water-wheel's cliff and hopping across a piece of flotsam.
Justice Toad refers to this item as his "legendary chest armor, the Hyper-Fabulous Jacket."
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