From the Super Mario Wiki
Woozy Guys (also known as Jumping Shy Guys) are Shy Guy sub-species that can do flips in the air. Woozy Guys appear Super Mario World 2: Yoshi's Island, its remake, Yoshi's Island: Super Mario Advance 3 and its sequel, Yoshi's Island DS. They flip and jump like the regular Shy Guys of Paper Mario. They appear in the Island Museum from Yoshi's Island DS. They reappear in Yoshi's Woolly World.
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