Honeyclimb Galaxy is accessible from the Bedroom observation dome. You need 42 Stars to enter.
Star 1: Scaling the Sticky Wall[edit]
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 
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 ability once you hit one and fall. So after a meteor shoots, quickly get past it. The first part, there are five honeycomb pieces. On the third piece, they shoot one meteor at a time and on the fifth piece they shoot two. Just get on the fourth piece and after the fifth piece sends down a meteor twice, get past it. Now there is a part of the wall three 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 separated, and Mandibugs between them. Fly over them to the star.