Shady Paratroopas are ordinary Shady Koopas with wings. After Mario or his Partner jumps on them, or a quake attack, like a POW Block, is used, they lose their wings and become normal Shady Koopas. Like KP Paratroopa, you only fight one Shady Paratroopa for the whole game.
The Shady Paratroopa also has unused data in Super Paper Mario.