Eater of Worlds
The Eater of Worlds can be summoned by breaking three Shadow Orbs (purple orbs that can be found deep underground in Corruption biomes) or using Worm Food (15 Rotten Chunks & 30 Vile Powder. Vile powder is made from Vile Mushrooms which grow in corruption biomes).
Quick Tip: When breaking Shadow Orbs, the first and second orb you break should be in hard to reach places. Leave the third Shadow Orb near a decent area or near your Arena so you don't have to travel far to get back.
IMPORTANT! DO NOT leave the Corruption biome when battling the Eater of Worlds. Doing so will cause him to retreat and despawn.
The Eater of Worlds is most likely the easiest real boss there is in the game. It is very large worm type enemy that behaves similarly to the various worm enemies you may have encountered while exploring underground.
Like those worm enemies, it is segmented which is its biggest weakness. Each swing of a weapon like the upward arc broadswords do hit all the segments they connect with. If you are confident in your ability, you may even defeat it without an Arena provided the spot you find has decent wiggle room.
Its weakest spot is its head but this also where it does the most damage. So be careful when aiming for its head. If you manage to damage one of its segments that isn't its head or tail, it will split and grow into another worm. This may seem like bad news at first, but it also will have two more weak spots.
There is a great window of opportunity when it splits though. When it splits, the part which gets left behind takes some time to get going. This is a wonderful opportunity to wail on its head continuously. Just keep going at it and the Eater of Worlds, indeed, will have bitten off more than it can chew.