Eater of Worlds

The Eater of Worlds is a Boss monster summoned by using Worm Food in The Corruption (manually planted corruption doesnt count) as well as being summoned each time you break 3 Shadow Orbs.

Each body segment has a chance of dropping Demonite Ore or Shadow Scales. When completely killed it will drop about 110 Demonite Ore, 90 Shadow Scales and 1.5 gold, a piece of Shadow Armor and some Lesser Healing Potions.

Strategy
The Eater of Worlds acts like a larger Giant Worm, spending most of its time digging through the ground with a distinctive sound before emerging in an attempt to ram the player. Because of its large size and multiple body parts, Vilethorn, Ball 'O Hurt, and other fast area of effect weapons are highly recommended, as the player can attack multiple parts of his body at the same time.

If you kill a section of its body, it will split into an additional worm with the head of the new worm starting where you destroyed the segment. The more worms that are out, the harder he is. The smallest size it can split into are 3 units and killing any part of that worm will kill it. The Eater of Worlds is defeated once you kill each segment.

Failing to kill the Eater of Worlds will result in the creature chasing you back to spawn, with some delay depending on how far away you were when you were fighting him. He will relentlessly attack until you slay him. After some time he will disappear if you keep dying (an "Eater of Worlds is Defeated!" message will appear with no loot dropped). Occasionally, only one section will follow you if you die, and you can obtain a piece of Shadow Armor relatively easily.

Standing on a wide, elevated platform (with either glass or sky below it) helps tremendously, as you can see him approaching from below.

Another strategy (in fact a really, really easy way to defeat this boss) is to collect a load of Vile Mushrooms, craft them into vile powder at an Alchemy Station, and just spam vile powder once The Eater of Worlds is summoned. About 100 - 130 Vile Powders should be enough, and it kills the boss very quickly.

Another easy way to kill the Eater of Worlds is to destroy the third shadow orb before using a mirror to retreat back to spawn. This allows you to resume the fight quickly and in familiar territory, as well as having access to healing if needed. Weapons that hit multiple times like a flail or Vilethorn make the boss easier as well.

Video of how to beat the Eater of Worlds (features new boss music):

Fastest method to kill the eater of worlds and useful advice

Note: Rocket boots can help immensely at dodging the Eater of worlds when he spawns on the bridge. Alternatively less geared players can have a second tier of the bridge made of platforms to jump onto, the Eater of worlds cant get up and turn around fast enough to get you if you do this.