The easiest level I found to do this in was level 16.
First jump onto the top box on your left. Then press X to attach and move onto the first button. After press B to separate yourself from the box. Next grab any box from the start (X) and go to the far right. Then jump onto the box in the top right. Attach (X) yourself to the box. Finally jump onto and attach to the rest of the boxes in the level.
The achievement will pop once you are attached to all 6 boxes - you do not have to finish the level.