This one is missable.
Take note of the symbols on the Metro at the beginning of chapter 6. It's an S in a shield, a face and socks pointing left, but they look a certain way.
Go right and grab the wings. Solve the light puzzle above the door, but do not enter the door. The solution is:
Go back to the ladder. Give them to the Unicorn, and it becomes a pegasus and flies away. There's a puzzle behind. The solution is (left to right):
Blue 3, Red 1, Red 2, Blue 3, Blue 2...
Blue 1, Red 1, Red 2, Red 3, Blue 3...
Blue 2, Blue 1, Red 2, Red 3, Blue 1.
A second ladder goes up. You'll see a balloon flier at the bottom of the screen, but only if you solved the light puzzle first. Take it and go up the second ladder.
Put the flier into the machine at the top, and a balloon will fly to the top, where there is a plane. Make sure you have the same symbols, then click the right arrow.
You need to do this (and other things) to get to the hidden level and earn this: