CURRENTLY UNOBTAINABLE SINCE LATEST UPDATE.
Update 0.16 fixed it.
You can get all of the required items in the achievement world. Achievement worldsEdit: I've also added a version of the achievement world where the setup is there for the "inception" achievement. You need to hit the lever on the left first. Then place a redstone on top of the piston on the right, and hit the lever on the right twice.
The items needed:
-1 normal piston (4 cobblestone, 3 wooden planks, redstone and iron ingot)
-1 sticky piston (normal piston + slime block)
-1 lever (you can make this with a stick and a cobblestone)
- around 10 redstone
You can smelt iron ingots from the iron ore in one of the chests. There's cobblestone in plenty of chests. There's redstone in the chest for the "dispense this" achievement. Slime can be found at the trampoline. Wooden planks can also be found in multiple chests. The pistons and the lever have to be made at a crafting table.
Place the normal and the sticky piston next to each other. (thanks to thoric) The wooden sides of the pistons should be facing each other. (one of which is sticky, the other one is not). place the lever a couple of blocks away (2 or 3). Now make a trail of redstone from the lever towards the regular piston. Then press the lever, and the piston should expand. Now destroy one piece of redstone from this trail, and make a trail from the sticky piston towards the lever. Now press the lever once to push the other piston away. Press the lever once more to pull the original piston back. I'm 90% sure that's how I got the achievement, though let me know in the comments if this works, as I did try some other things, and the achievement does not pop instantly.