I cant jump to the third mushroom. What am I doing wrong.

all you need to do is make sure almost immediately after you jump to flap out your cape which will make you jump further... also, stay on the side farthest from the mushroom you're jumping to so it leans back and then the side you jump off of will be higher allowing you to have an easier time getting to the mushroom.
after you get to the mushroom, you must quickly use your bat-grip thing (forget what it's called)... you'll know what i mean when you get there. if you aren't very quick, you'll fall off the mushroom.