In order to find the hidden level, you need to do several things:
In chapter 6, find the balloon and fly away in the plane. This earns you:
In chapter 7, take the blue pill. You will miss the 8th chapter, so save before you take the pill.
In chapter 8, take the red pill. Then finish chapter 8, earning you:
At the end of the game, click on Secret at the main menu. Then click on the right picture. It will only be there if you've cleared all three endings.
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To clear the level:
Go left. Take the hammer from the statue and the flower from the pot. The solution to the door puzzle is:
Left, Up, Left, Left...
Left, Down, Right, Up,...
Right, Down, Left.
Go in the door. Use the hammer on the jar with the worm. Take the worm. Go upstairs.
Pu the worm in the man's hair, then flip the switch behind him. Go right.
Give the flower to the robot. Click on the red/black panel. The solution is to get to the bottom right while all the lights are green. A solution is:
Right, Down, Left, Down...
Right, Down, Left, Down...
Right, Right, Right, Up...
Left, Up, Up, Right...
Right, Down, Left, Left...
Down, Right, Down, Right.
Then click on the numbers above the door. There are 5 numbers, and each has 5 positions (Top, upper middle, middle, lower middle, bottom). The solution is:
1: Middle
2: Top
3: Lower middle
4: Upper middle
5: Bottom
Go through the door, and you've cleared the world!