red caps can be found in quite a few areas of the freeplay map as well as during a few of the actual levels as well.
They at first appear to be the red mushrooms, but pop up on proximity or being hit.
Places that they can be found are:
Thestral area (through garden at hagrids hut)
Path from station to Hogwarts
"A Giant Virtuoso" (thanks futrstyl)
this is probably not a full list but where you can find the most.
just find 30 and the achievements your's.