Walk onto the other side of the starting planet. You should now see a dark castle figure. Climb the tower and talk to the luma at the top. Use the sling star and the launch star to get to the next planet.
Once at the next planet, dodge the rolling boulders and collect the 5 star chips. Use the launch star to get to the next planet.
At the bean shaped planet, time your attack and Star Spin the Piranha Plant.