This stage is fairly simple if you know how to proceed. The goal of your first shot is to kill the pigs at the bottom left, bottom right, and upper right. Launch into the bottom right planet.
Power Activation Point
Shoot out your laser guns into the metal platform as you are passing through. Note that this shot can kill pigs at the upper left planet too, but they are not necessary.
First Shot Result
Your laser gun kills the pig at the bottom left planet, and possibly the upper left. You crash into the TNT bomb of the right planet, setting up explosion of the head piece.
Launch the Princess with the path shown in the picture.
Second Power Activation Point
Pull the meteor to kill the satellite, note that you will need to pull that into the upper planet if you failed to kill them with your first shot.
Second Shot Result
All the pigs are dead and you will end up with the three star mastery rating.