Brain of Cthulhu

The  is a boss that was added in the 1.2 update. This boss is a replacement for the Eater Of Worlds if a world has The Crimson instead of The Corruption.

It is the second body part of Cthulhu to be put in the game, the first one being the Eye of Cthulhu.

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It has two phases, and currently seems to resemble Ocram in how it behaves. In the first phase, it teleports around the player's vicinity, surrounded by enemies called Creepers, which randomly charge directly at the player. The Brain is completely invulnerable during this stage. Once all of the Creepers are gone, the front of the brain opens up, revealing a heart with an eye on it, as it enters stage two. The Brain's attack and speed dramatically increase at this point. Once all of the 1000 HP have been exhausted, the Brain is defeated.

Note, the Brain can move through large blocks with ease and is quite large. If you are inside the small heart room (like to pick up the item said heart drops), the brain will spawn above you and trap you in the small enclosure. The brain will teleport down into the small room (even if the room is half its size) and can kill you very quickly. It might be a good idea to drop a bomb to blow up the third heart, then run to a clear open space to prevent getting trapped; at the very least, make sure you have your grappling hook ready or set up some platforms to quickly retreat to the main cavity. You'll need the extra room.

One interesting thing to note about the Brain is that it is the only boss in the game that does suffer from knockback during the second stage of the fight. Hitting it repeatedly will prevent it from reaching the player.

Unlike the Eater Of Worlds, the Brain Of Cthulhu or his creepers won't flee when out of the Crimson.

Preparation
If you have a world with The Crimson, you should probably already have The Undertaker by the time you face him (breaking the Pulsating Hearts gets you this weapon, and it almost always drops from the first Heart you break). Stock up on bullets; at least two hundred, to be safe.

A magic weapon is extremely useful here, if not entirely necessary. You'll need to gather fallen stars to increase your maximum mana to around 100 or more before rushing into the battle. You'll also need silver armor (or equivalent) or better.

To make a good early magic weapon, hunt for 8 Gems of a single type and make yourself one of the staves (Topaz_Staff, etc.; see Spells), depending on what metals are available in your world -- get the best one you can easily manage. This is the best weapon to use against the Brain at this stage of the game, due to it being able to pierce enemies and its low mana cost.

Build row upon row of platform in the large underground cavern in the Crimson. The staff and gun will help you fend off critters the happen across you while you're building. It will take 3-4 stacks of wood platforms to fill the space. Make them as far apart as you can reach without jumping; this ensures they're just close enough to reach with a single normal jump. You can place a platform every 2 blocks to save having to use more wood than necessary.

The Battle
Summon the boss either with the Bloody Spine or breaking Hearts with Bombs, so that you do not get trapped inside the Heart's cave by the Brain when it appears.

At the beginning, the Creepers will rush at you at first, simply avoid them and look for the main body of the boss. The Creepers always flock to wherever the boss teleports, so the easiest way to take them out is to aim straight at the main boss the whole time. This will also prevent Creepers from attack you for the most part, as you're firing where most of them are and taking out more of them than you would be if you only attacked the ones that came close.

Blood Crawlers and Crimera will come at you occasionally, but they cannot go down through the platforms. Use this to trap them and kill them without getting in harm's way. Prior to defeating the WoF, none of the enemies here have ranged attacks, so you need only avoid running straight into them. As long as you're a few levels up on the platforms, the Face Monsters aren't any danger either.

Keep an uninterrupted barrage of magic and/or bullets between yourself and the main body of the Brain the whole time, and keep on the move so that he doesn't teleport directly on top of you. When you're out of mana, switch to the gun and just keep shooting until your mana recharges. You'll catch all the Creepers and most likely any other stray Crimson monsters in the crossfire.

When all the Creeper minions are dead and he's vulnerable, continue shooting him and keep moving. He is affected by knockback, and the knockback is the only thing preventing him outpacing you. The platforms give you sufficient mobility to evade him 80% of the time, so use them. Always switch back to the staff when your mana's fully recharged, because staves tend to do more damage than the gun, and they can also hit multiple times with a single bolt if your aim's fairly decent. Although the projectile is slower than bullets, by this stage the Brain keeps quite close, so aim should not be a problem.

The platforms should catch most (if not all) of the Creepers' drops; wait until the boss is dead before you try to collect them all, to be on the safe side.

Another method is to set your spawn next the place at which you summon him and in the crimson, because he teleports to you as long as you are within some distance of him and in crimson he will teleport to you. Let him kill you and then when you respawn he will teleport to you attack him or his creepers whichever stage he is on with your max DPS weapon once he dies gather the drops and done, no potions necessary.