The achievement description is pretty self-explanatory. However, I will explain more for your understanding.
You can get this with one villager. You just have to trade with it repeatedly.
Natural emerald ore can only be found in the extreme hills biome, making it the rarest ore in the game. You will find it easier to start this process by acquiring emeralds from villagers, then using those emeralds to buy other items.
I find it easier to get a lot of emeralds from librarians, the villagers who wear white clothes. It is easy to mass produce sugar cane, and thus paper or books, which are items that librarians look for. Other villagers like blacksmiths (coal), butchers (meats), and farmers (wheat) are good for trading too.
If there isn't a village nearby in your world, you can get this with cured zombie villagers too. See my achievement guide on curing a zombie village for more information.
UPDATE: Start a world with the seed STOCKDR (v. 1.2.0.) to spawn in a large village with many villagers. This will make it easier if you don't have a village in your other worlds.