I noticed the defeated enemies count at the end of a level are not adding up.
I very carefully counted stomping on over 7 paratroopers. They went into their shells, stopped flying, and toppled off screen.
Is that not a "defeat?"
I have had the same question. Apparently, stomping on the paratroopers and koopas and seeing them going into their shell, is not a "defeat." The only way to kill them normally is if they are hit with another shell, or you have a Star active.