The game contains 3 literal easter eggs you can find! You only need to find a single egg - any egg - to get the achievement. An easter egg is registered as having been found once it's in your inventory. The achievement unlocks when you complete the game.
1. Heart Egg
In the library, go to the computer and enter the library database. Search for "ISBN 4755568135314". This should give you a result for a book titled "Mid-Break at Waverly". Next, exit the computer and go towards the stairs and double doors. Click on the bookshelves immediately to the left of the stairs and doors. Click on the large book in the middle there and open it.
2. Raven Egg
In the locked classroom with the wooden map of the United States, check the raven puzzle. Click once on the tail, twice on the wing(largest piece), and thrice on the eye.
3. Cat Egg
In the cellar, with the puzzle where you place the four gold stars, you must place them all on the only vertical bar with four slots. They must be in the following order, from top to bottom: Cat - Bug - Ape - Raven.
Extra:
If you use any egg on Leela and then ask her to play Air Hockey against you, you'll get access to a fifth and final mallet!