Borderlands

You will get this achievement from a special character located in the Hollow's End zone of the map. Specifically you will find him in the town of Hollows End. You will find this town at the far south-west of the map. Follow the road behind the gallows to a building with fyrestone written on top of it.

The quest is broken into five stages in which you must return a total of 435 brains to the quest giver. You can only collect the amount alloted for each stage,so do not bother collecting more brains than needed for each stage. A good tip is to leave all the extra brains on the ground so you can scoop them up when you start the quest or the next stage of it. In order to get brains you must head shot zombies and defilers for them.

Here are the amounts you will need for each stage.
1. Collect 10 brains.
2. Collect 25 brains.
3. Collect 50 brains.
4. Collect 100 brains.
5. Collect 250 brains.

As a further addition to the solutions above, one problem for some players has been actually finding the quest and the character who gives it.

The best ways I've found of doing so is to accept the "Pumpkinhead" mission from the Jakob's Cove bounty board very early in the game (about 2-3 quests in).

This quest will take you to a "boss" named Pumpkinhead, but it will also take you to within close walking distance of the area where this quest begins.

After killing Pumpkinhead, return to the nearby township area - really just a collection of buildings - and look for the gallows. Behind the gallows is a path which leads around and to a house. The quest begins with the character in this house - the identity of which will become very obvious very quickly.

Getting into this quest early allows you to get shooting and get through some of the early stages of the 5-part quest before you are too far into the story line.

As mentioned above - the 10, 25 and 50 brain sections of the quest can be done very quickly in the areas in the area ... plenty of zombies there, and as you progress up to meet Dr Ned for the first time.

Once you get the 100-brain quest done, scuttle back to the house and turn in as you have for the three previous parts, and just get going with the story - you'll shoot way more than 250 zombies throughout, allowing you to get this quest done and get the storyline underway as well.

Final point - these zombies are pretty slow moving - you can actually run past them sometimes with them unable to catch up to you. Use this to your advantage - draw them into preferred killing zones or bottlenecks to allow you to headshot them (I favour a pistol with zoom function and extra damage class mod myself).

Zombies can be headshot easily from up on high as well, as there are areas where you can stand above them, take a minimum of damage and shoot them as they mill around ala a George Romero movie.

Credit for this video goes to Mr360Games. You need the Zombie Island DLC to obtain this. The quest starter is in Hallows End (location in video) and you have to give TK his leg back which is basically infront of his house. After that you have to obtain 10, 25, 50, 100, 250 brains ANY BRAINS YOU COLLECT BEFORE STARTING THIS MISSION DO NOT COUNT

This has probably already been mentioned somewhere, but the zombies are particularly weak against incendiary weapons, so any weapon that causes fire will hurt them more. On the other hand, they are resistant to corrosive weapons, so avoid those when looking to dispatch many zombies quickly.
Currently I am going through the zombie island with an incendiary machine pistol to cover a couple of the challenges quickly (kills with a pistol, incendiary kills, human kills, critical hit kills, and pistol proficiency are all taken care of with this gun in this area).
Yes, I know at the time of posting I don't have this achievement yet, but I will very soon, just about twenty brains away. I ran out of time this morning before I had to go to work.
Edit- Got it. Its so much fun watching the brains fly out of their head.

The fastest way I have found to do this is spawn in jakobs cove and from the spawn point make your way toward the lumber yard. Once at the lumber yard press start and exit your game, and then just start your game back up it will put you at the beginning at the spawn point it will save all your brains. Keep doing this I was getting over 100 brains per run easy.

Some tips that helped it go a little faster is change your sensitivity to very low and use a decent revolver and just hip fire the small reticle makes it easy to hit the head.

What really helped me in harvesting brains was a handy shotgun, since they do large damage up close and you could easily run up to a zombie and shoot it in the head, and out pops the brain.

The Braaaaaaaaaaaaains! mission is a side quest line given by 'Zombie TK Baha' who can be found far west of 'Hallow's End'. I highly advise you go meet Zombie TK Baha on your way to the waypoint of the third mission 'House of the Ned' so that any zombies you kill throughout the DLC will count. Now once you've met Zombie TK Baha he will give you the mission quest line, there are 5 missions that all revolve around collecting a set number of zombie brains to give to TK. In order to get zombie brains you need to kill zombies by headshot so grab your best sniper rifle/assault rifle/SMG/Pistol and aim for the head. Every zombie counts and I advise you to return to TK the second you gather enough brains to complete each mission to avoid wasting time grinding at the end.

The 5 missions are:
◾Brains - 10 brains
◾Braaains - 25 brains
◾Braaaaains - 50 brains
◾Braaaaaaaaaaaains - 100 brains
◾Braaaaaaaaaaaaaaaaains - 250 brains