In order to unlock this achievement, you will need a bow, which can be crafted with:
- 3 Sticks: You can craft 4 sticks with two wood planks.
- 3 String: String can be obtained by killing Spiders, which spawn at night time if you are playing in easy or higher, and Cave Spiders, which are poisonous spiders that spawn in mineshafts (wooden structures found underground.)
Now that you have all the required materials, you can craft a bow. Now, you will need some arrows.
Arrows can be crafted with:
- 1 Stick: You can craft 4 sticks with two wood planks.
- 1 Feather: Feathers can be obtained by killing chickens. Baby chickens do not drop feathers, only adult ones do, so if you want feathers from a baby chicken feed it a lot of seeds until it grows up then kill it.
- 1 Flint: Flint can be obtained by mining gravel blocks. These blocks can be found on the ocean floor, near lakes, and underground in caves.
Now that you have all the required materials, you can craft 4 arrows, which should be more than enough to kill a creeper.
Now, you will need to wait 'till night time while keeping your difficulty easy or higher, so Creepers can spawn.
Once you find one, try hitting it a few times with your bare fist to lower its health while being careful that it doesn't detonate by straying back after every hit, then you can shoot it with your bow by pressing and holding then releasing
.
If the Creeper dies, the achievement is yours.
Here's a video, just in case: