First off, this achievement requires you to "Kill a rare enemy of all the following types." Rare enemies are the ones with yellow names that have minions following them, not the blue packs.
Savage Beast - Fields of Misery, Southern Highlands, and Northern Highlands. All have a waypoint in them, just load a game with the waypoints, clear, reset if you don't get them.
Harvester - Cathedral Level 4. Load a game with the Cathedral level 3 waypoint available, go down and enter level 4 (They are always really close together, its the level you killed Jondar on). Once you clear level 4, just exit the game. When you reenter it will place you at the beginning of the level.
Imp - Defiled Crypt. Load a game with the Cemetery of the Forsaken waypoint, and clear all 3 crypts.
Enraged Phantom - Festering Woods. Waypoint.
Savage Fiend - Cursed Hold. These guys only spawn on the outsides, middle, and between the cells. I have never seen them spawn inside the cells themselves. Load a game with Halls of Agony Level 2 way point, clear to and then through the Highlands Passage to the Cursed Hold. After clearing the Cursed Hold, run to the end of it, and there is a Checkpoint at the top of the stairs leading to the Halls of Agony Level 3. Once you activate it, exit and reclear the Cursed Hold from there.
Quill Demon - Scavenger's Den Level 1. This dungeon is linked to Fields of Misery. Unfortunately it doesn't spawn every game and may take multiple tries to get the dungeon, and then after that you aren't guaranteed to get a rare mob. May take a while.
Scavenger - Defiled Crypt, Fields of Misery, and The Weeping Hollow. Large area you can find these guys. You can either limit yourself to one, or you can leave New Tristram through the Northwest Gate and clear Weeping Hollow, all the Defiled Crypts, and Fields of Misery. Large area to cover, but they all have a chance to have this one, so why not take advantage of it?
Skeleton - Cathedral Level 2-4, Cemetery of the Forsaken, Defiled Crypt, Fields of Misery, The Royal Crypts, and The Weeping Hollow. Unless you ONLY need these guys, don't try and farm for them. They are in so many locations you will probably get one while farming for the other, more select, mobs in the areas they inhabit.
Skeletal Archer - Cathedral Level 4, and The Royal Crypts. Rare and Champion mobs are rare in The Royal Crypts, or they have been for me. I would reccomend farming for them using the same method listed for the Harvesters.
Returned Archer - Drowned Temple and The Festering Woods. Farm using The Festering Woods waypoint.
Arachnid Horror - Caverns of Araneae. Run here from the Wortham Chapel Cellar, and then there is a waypoint outside of, inside of, and at the end of the Caverns. Clear the map and then just leave the game and hit Resume.
Dark Berserker - Halls of Agony Level 1, 2, and 3. I would suggest just using the Leoric's Manor waypoint and walking to the Halls of Agony Level 1, and then clear levels 1 and 2. They spawn in level 3, but you need to traverse through Highlands Passage and The Cursed Hold to get there. Faster to skip that level.
Dark Cultist - Every zone from Southern Highlands on. Another one that unless you ONLY need this one, don't farm for it. You will probably find one while searching for the other more zone selective mobs.
Unholy Thrall - Although these CAN appear on any level of the Halls of Agony (Due to the Dark Vessel mob), I BELIEVE they can only SPAWN (And therefore be champion or rare) on Halls of Agony Level 1. Use the Leoric's Manor waypoint and walk to Halls of Agony level 1.
Disentombed Hulk - Halls of Agony Level 1 and 2. Use the same suggested method as Dark Berserker.
Hungry Corpse - The Weeping Hollow, Cemetery of the Forsaken, and Defiled Crypt. Use the same method as Scavengers, except include Defiled Crypt, and exclude Fields of Misery.
Retching Cadaver - The Weeping Hallow, and Defiled Crypt. Same as Hungry Corpse, except you won't find them outside the Crypts.
Ravenous Dead - Cathedral Level 1, Cemetery of the Forsaken, Defiled Crypt, Fields of Misery, and The Weeping Hollow. Best place would be to use the same as the above 2, and Scavengers.