I exported my world just before I got this achievement so others could get it too.
If you download and import this world you will start on top of a small pole of sand. There is a Zombie Villager at the bottom of the pole. In your inventory there is a splash potion of weakness and a golden apple. Throw the splash potion at the Zombie Villager and he should get red particle effects around him. Next, feed him the golden apple.
EDIT: Some people are having a problem getting the apple to work. Try getting rid of the topmost piece of sand you are standing on so you are nearer him
EDIT 2: Some people are struggling because they are throwing the potion/feeding the apple to a regular zombie. The Zombie villager is noticably different looking with a larger head nd a protruding noseEt voila.
I'm not sure if you get the achievement straight away (my notifications don't always pop up) or if you have to wait until he finished being cured (takes about 3 minutes)
If you head up to the village and enter the blacksmiths you'll find some other stuff in the chests that may help you get other achievements
You can pick up the blaze rod to get
If you turn that blaze rod into blaze powder and collect the glass bottles, nether wart and glowstone from the chest, you can use the brewing stand to make a potion. Fill the bottles with water, put them in the brewing stand, add the netherwart, then add the blaze powder, then add the glowstone, then take out the potion to get
Drink this potion and use the diamond sword to jump attack a mob to get
There is wheat to make bread, wools and other things you may find useful there too
A couple of houses down, there is a nether portal which takes you to a ledge over a lava pit where ghasts regularly spawn, a perfect place to get
If anything goes wrong, delete the world and import again to get back to the pole above the Zombie Villager
Here is the file...
http://www.houst.co.uk/mc/ZombieDoctor.mcworldHope it helps