Firstly, acquire a bow (using a crossbow will reportedly not work). The easiest way to do this is by crafting one, using 3 sticks and 3 pieces of string. You could also try killing Skeletons as they drop bows on occasion.
Next, you'll need arrows. Again, the easiest way to get these is by crafting them, using flint, a stick and a feather (for 4 arrows). You could again try killing Skeletons as they will often drop arrows.
After this, find a Creeper, which will only spawn on Easy difficulty or above. Get near it, being careful that it doesn't blow up, and get it down to low health (a couple hits with a stone sword).
You can now use the bow to kill the Creeper, which should die with one arrow. You should now have the achievement.
Hope this helps!