I followed this guy's video to get the achievement. His video is like 17mins long because he plays sloppy and isn't sure where to go, but I was able to get it in less than 5 mins, and if you play better then you can get it even quicker.
Basically once you have placed the purple block and gotten the tree out of it, go back to the purple level and grab a purple cube, then head to the next area as shown in the video and take the purple up the corridor and finally into that secret room and open the door, the puzzle inside is pretty easy, you just need to get the timing right in order to cross with the green cube and