In order to completely purify a world, you need to remove every crimson, corruption, or hallowed block from your it.
A tried and true method for this is to load up a brand new small world, make many hellevators throughout it, and fall down each of them shooting green solution out of a terraformer.
You can get the terraformer by purchasing a clentaminator from the steampunker npc for 1 platinum, and dropping it in a pool of shimmer. You can also buy green solution from the steampunker npc for 15 silver each.
A website that I would extremely recommend using is TerraMap (
https://terramap.github.io). This site will allow you to upload your world and search for any corrupted/hallowed blocks, giving you their precise location.
You'll get the achievement once your world is 100% purified and you ask the Dryad npc about "status".
Good luck!