Super Mario Galaxy 2/Honeybloom Galaxy

Star 2 (hidden): The Secret Wall Jump
Enter mission 1 and go up to the first swing in the level. Instead of swinging to the other platform, swing high enough so that you fly up to the wall that is embedded in wood. From there, quickly wall jump until you get to the very top of the area. The power star will be there waiting for you.

Green Star 2
In area 3, go up past the launch star past the swing vine. Fly all the way up to the green star to obtain it.