During stage 8, you will acquire a platypus. You can only use the platypus when you are using the dragon character. The Platypus is moved using the right analog stick.
You'll come across small little caves in just about every stage. They are about half the size of the girl and the top is arched. If you move the platypus into these, you'll get a view of the inside of the hole and you'll be able to move the platypus around inside the cave. You'll need to enter ten of these for this achievement.
Once you start your game and choose the difficulty, you'll be at the stage select screen, you can press Y here and get stats, including the amount of platypus nests you've been in. Note that stats in goddess and initiate difficulties are not shared, so you'll need ten nests in one or the other.