To make a dispenser you need:
1x Bow
1x Redstone
x7 cobblestone
to make a bow you need 3 string and 3 sticks and place them like so (O: nothing, S: stick, L:string):
OSL
SOL
OSL
Then once you have a bow, x1 redstone and 7 cobble stone place them in the crafting grid like so (R: redstone, C:cobblestone, B:bow)
CCC
CBC
CRC
I don't know if you actually have to place the dispenser somewhere, or if it unlocks after taking it from the crafting bench, but the achievement only unlocked for me after placing it.
You do not need to place the dispenser, just craft it. The achievement may take a while to unlock, for me it took over a minute.