EDIT: A couple people in the comments say that you can find these fragments before you build the room, I just did not come across any before that.
You will first need to unlock the Theme Workshop. I believe you need between 40-50 dwellers to unlock it (I don't remember exactly) and it costs 3,200 Caps. Once you build the room, you unlock the ability to find theme recipes on quests and in the Wasteland.
You can find these fragments on quests and in the Wasteland at any time. Once you find all nine recipe fragments, you will unlock this achievement. They are harder to find than junk, outfits, and weapons, but they are not super rare or anything. You can find them on the bodies of enemies or in the glowing areas of the vaults you are searching.
You can also instantly purchase all nine fragments using ~27 Nuka-Cola Quantum. You can find Nuka-Cola on quests or you can purchase some from the shop for real money.