***STORY RELATED: Cannot be missed***
Once you've collected the purple beam and have made your way back to the blue gate, use the purple beam to propel yourself over the gate (you can connect the purple beam to the wooden beam above the gate, then hit
to pull yourself over).
Once you land, one of the blue people will automatically steal yourself, unlocking the achievement!
(Side note in case anyone is stuck on this next part: to pass by the scanners leading to the next area after your stuff is stolen, you have to turn yourself blue with the paint machine nearby. Use your pickaxe to destroy the block on top of the button, as well as hit the tree with the blue leaves that's direclty above the entryway of the paint tub to turn the paint pipe blue.
Then, as the red man is running back and forth, use your purple beam between two stumps to block him from running past the button. Instead, he'll run into your beam and onto the button, allowing you to stand on the paint table and turn yourself blue. This will then allow you to bypass the blue scanners and access the next section! Just thought I'd share this in case anyone else was stuck