Green Star 1: Wall-jump the sixth gate once it's rising to get the star.
Green Star 2: Pass the gates to the right of the Warp Box by jumping after running at full speed and get the star. Do the same way back.
Green Star 3: By the cloud, be in Cat form to spin the wheel that raises a platform. Climb that platform to get the star.
Next to the clear pipe after the checkpoint, there's a Cat Luigi stamp. Get it by either climbing the wall in Cat form or ground-pounding the cloud above.