(Information taken from:
http://terraria.wikia.com/wiki/NPC)
The full list of NPC's and how to unlock them are:
The Guide: is gained at the start of any map. He is the first NPC you will have.
Merchant: is acquired when all players combined have a combined wealth of more than 50 in their inventory.
Nurse: is acquired when your character has found and used a Heart Crystal.
Demolitionist: is acquired when you have an Explosive (i.e. Bombs, Dynamite etc.) in your inventory.
Arms Dealer: is acquired when you have a Gun in your inventory.
Dryad: is acquired after you have beaten your first Boss in that world.
Old Man/Clothier: is acquired after defeating Skeletron at the entrance to the Dungeon. The Dungeon is at the opposite end of the world from the Ocean.
Mechanic: is found bound within the Dungeon.
Goblin Tinkerer: is found bound within the Dungeon, the Underground Jungle, or simply Underground after defeating the Goblin Army.
Wizard: is found bound Underground after you have beaten the Wall of Flesh. He can also be found bound in the Dungeon
Steampunker: Will appear once the player has killed any Hard Mode boss and there is a suitable house for her.
Dye Trader: Will appear once the player has any type of dye material and there is a suitable house for him.
The Party Girl: Will only appear with a 9% chance every day once the player has at least 8 NPCs and there is a suitable house for her.
The Cyborg: Will appear after defeating Plantera and there is a suitable house for him.
The Painter: Will appear after at least 3 NPCs have moved into your town and there is a suitable house for him.
The Witch Doctor: Will move in after you have defeated Queen Bee.
The Pirate: Will arrive after the defeat of the Pirate Invasion and will move in after you have suitable housing for him.
The Stylist: Is found bound in Spider Caves. You must right click her to unbind her.
Santa Claus is not needed to get the achievement (Thanks Sh0ck for confirming.)
Once you've got all of these characters living in your house, the achievement should unlock.
NOTE: NPC's who die will respawn after a while. It won't stop you from getting the achievement.
Edit: Thanks to iMaginaryy for confirming you can get this in someone elses world! :)
Edit2:
This is currently unobtainable until a patch is released. One of the new required NPC's is the Cyborg. He will not spawn until you beat Plantera, which cannot spawn because of a glitch.
Thanks to Draco719 for this info. :)
Edit3:
This has apparently been patched, but if someone could confirm it is fixed, that would be great. :)
Also edited the guide with all the new NPC's other than the Travelling Merchant and the Angler, since I don't believe they count, if someone could confirm this too, that would be great. :)