So you're working your way through Yooka-Laylee, breezing through the first two worlds, and now you're walking around Hivory Tower only to find that you don't know where the heck the third world is? We've been there.
World 3 is actually in a place you've already been - the Archives. This is just to the left of the path that takes you to the second world, and it's right before you reach Rextro's arcade in the Hivory Towers. You've probably already been there, the place with the endless shelves of books, a giant aquarium, etcetera, but go back after you've beat the world 2 boss, and you'll see your good buddy Trowzer there.
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Talk to Trowzer in the Archives after beating the World 2 boss, and he'll open up a panel in the bookshelves that will take you to World 3. And that's it. Happy flapping around!