There are two puzzle rooms available but first they must be purchased by Daydreaming for each floor of the dungeon to spawn on the corresponding floor. Complete 15 of these to unlock the achievement.
The first puzzle is called the Puzzle of Revelation and looks like this
You must activate all the orange circles bar one. The lit up circles surround the bad circle, but there's no consequences for failing, it will just randomize the puzzle.
The second type is the Puzzle of Connection and looks like this
The goal is to rotate all the platforms until all the lines are connected and it all turns orange like this