Upon picking this star and being placed in the course, head to the right and follow the edge past the tree warp you might have used in the first star. As you continue along, you should notice a slightly different, but familiar, foe on a platform sitting above a frozen pond. Go up the nearby slope and do battle with the Chill Bully, which is no different than the ones in Lethal Lava Land. Jump Kicks are still the best option for pushing them back, but you do have to contend with the icy platform here.
Note that if you get knocked into the waters below, you will notice the pond directly below the Bully acts like lava. So, Mario will take damage upon making contact and should you get trapped underneath the icy arena, then that pretty much means you’re going to lose a life. The gist of this star is just knocking the Chill Bully off of the platform, which unlocks the star.