Complete the final level of the game, then start it again and die. You will be transported to the secret level.
Enter the door on the right and keep walking forwards until you reach the wall with cubes spots (it'll be on the left). Use the 4 supports to your right to parkour over and get 2 cubes.
Head back out and use those cubes to climb up the wall (to the left of where you started). From the central platform, use the support pillars to grab the 2 more cubes. Be sure you have all 4 cubes before proceeding.
Quickly head across the elevators and complete the circuit, then climb said elevators to reach the exit. You have to move faster than they raise or you'll have to retry.
Afterwards, you will receive the achievement - the last one in the game.