The key to solving the rest of the puzzles on this screen is having someone to help you.
You'll need to help hatch something to get that help (no, not the boucassier).
Look in the store for a boa-boa egg. If you can get the egg to hatch, you'll have the help that you need. (See the hints about the store if you don't yet have an egg.)
Again, you need to incubate the egg.