Honeyclimb Galaxy is accessible from the Bedroom observation dome. You need 42 Stars to enter.
Star 1: Scaling the Sticky Wall
You can only use Bee Mario to climb the honeycomb wall, so get the Bee Mushroom. There are some unattached honeycomb wall parts, so press and hold A to fly. There is a huge space with a ? coin, so grab it and honeycomb wall platforms will appear. Grab onto them and you will make your way to the next part.
Now there are meteors. Don't hit them--you'll lose your Bee abillity once you hit one and fall. So after a meteor shoots, quickly get past it. The first part, there are 5 honeycomb pieces. On the 3rd piece, they shoot 1 meteor at a time and on the 5th piece they shoot 2. Just get on the 4th piece and after the 5 piece sent down a meteor twice, get past it. Now there is a part of the wall 3 pieces long, with meteors coming down from all of them. Quickly fly above it and get back to the wall, and watch out for more on your way to the Launch Star.
Now this is where the Star is, but there are now tons of Mandibugs. Since they're on the wall, they can't be killed. So fly above them when they try to ram you. There are now moving honeycomb platforms with Mandibugs near them, so watch out. Now there are tons of honeycomb pieces seperated, and Mandibugs between them. Fly over them to the star.