This achievement can be easily unlocked in the tutorial area.

After completing/skipping the tutorial, make sure you have a crafting station, and head up the stairs, you'll see a chest with a bow in it. Don't use the bow, if it lowers in health you cannot craft it.

Now head into the building on your left with the anvil above it. Open the chest, take out a pickaxe, mine 7 nearby cobblestone blocks.

Now exit the building, and go left and straight until you see stairs leading into an underground area. There is a picture frame of redstone on the side of the entrance. Break it.

Now plop down your crafting table, go the the mechanisms tab, and make your dispenser.

If you need any help feel free to Pm me.