Can I defeat the Eater of Worlds with only Iron Armor and a Demonite Broadsword? if not, what do I need?

You've got a number of options open to you (aren't sandbox games grand!):

• You could go mine out some better ores. For instance, you should be able to dig a shaft, find Silver and/or Gold, and mine enough to make better armor.
• You could go into the Jungle and try to make some gear - the Thorn Chakram is easy to recommend. Jungle Armor might be tricky, as the resources required are likely going to be difficult to collect in quantity at your current health/armor level. The Chakram is pretty straightforward and low resource cost, though.
• You could fight the Goblin Army, which has a chance to spawn after you start breaking Shadow Orbs. They drop Harpoons, which are recommended for use against the pre-hardmode bosses and apparently make pretty short work of them. The Army's not tough to fight if you have a pretty defensible area and a fast-firing weapon that does decent knockback.

I'd also suggest constructing a boss arena (in the corruption, if that wasn't already clear) if you haven't already. It doesn't need to be particularly long or tall - 75 or so blocks wide and two jump-heights high should be enough. Just put wooden platforms around the inside so that you can maneuver should the Eater dive through it.

Preferably, your ideal weapons are weapons that pierce through multiple enemies, weapons with fast swing times, or weapons that can hit multiple times.

First Time

Armor When it comes to armor, you'd be hard pressed to find ores. At that stage of the game, the best armor you can get is either Gold or Meteroite* armor. If you play a more Melee approach, it's best to use the Gold armor, as the set bonus grants a +3 defense. If you play more Ranged based approach, using Meteroite Armor + Space Blaster can work wonders.

Basically, your choice of armor all comes down to your playstyle, Melee or Ranged.

*Only happens under certain conditions

Weapons I find that weapons with big hitboxes work better than other weapons for the most part. Weapons that are easy to find at this level include the Blade of Grass, and the Gold Broadsword. Not to mention, coupled with a decent swing speed, the Blade of Grass has a 25% proc chance of causing poison, which can greatly help with your fight.

Misc It's advisable to bring Accessories that grant health regen, for example, the Band of Regeneration. Bring potions. Always bring potions, because you never know what you need. Ironskin potions also work wonders, granting extra defense, which increases your survivability.

Farming

A trick I use is to combine high tier armor (typially Shadow), combined with a Flail (You can find these in Chests), combined with wooden platforms, allows you to quickly take him out without dying too easily.

This is my entire process on how I've beaten the eater of worlds. It is not my intention to brag, but instead provide credibility; using these exact steps, I have defeated the eater of worlds using a brand new hardcore character without the assistance of any other players or items.

1. Obtain all of the following:
   • At least iron armor (or better) - set bonuses help
   • Gold bow
   • 250-500-ish arrows (some flaming arrows greatly help)
   • several suspicious looking eyes
   • several vacant houses for NPCs
2. Brew several archery potions, ironskin potions, regeneration potions, and healing potions
3. Under the effect of all buff potions, summon the eye of cthulhu and defeat him. Depending on how fast you are at this point in the game, you may or may not be able to defeat more than one per night. If the moon is past the halfway mark in the sky, don't summon another until the next Terrarian night.
4. After obtaining enough demonite ore, craft a war axe of the night and demonite bow.
5. Talk to the dryad to obtain purification powder, or the demolitionist to obtain bombs, and head over to the corruption. using either to access shadow orbs, break 3 of them (keep in mind the third will summon the eater of worlds). If any of these drop from shadow orbs, you can use them as weapons:
   • Musket - an excellent ranged weapon, especially for this stage of the game.
   • Ball O' Hurt - An excellent weapon to fight against the eater of worlds. Definitely a good idea to use it during the boss battle.
   • Vilethorn - if you have any mana, using this whenever possible is highly recommended. Cast it parallel to the eater of worlds' body for maximum damage.
6. When the eater of worlds is awakened, you'll want to be equipped with the following for the boss fight:
   • War axe of the night
   • Several ironskin potions, regeneration potions, and healing potions
   • Several grenades, if possible (arrows or musket would work too)
   • Any shadow orb weapons, and an ample supply of mana if using the vilethorn
7. Chances are you'll be in a pit, and this is actually a good thing since it protects you from any eaters of souls (which are a nuisance during the boss fight). Use several wooden platforms so you can navigate vertically, and start swinging your war axe or flail.
8. During battle, simply move next to or below his body when it attacks you so you can deal constant damage with your weapon. If you're confident you aren't going to hit yourself, lob a couple grenades, as they do a hefty 60-ish damage to multiple segments.
9. As segments die, they drop hearts, which are instantly collected at melee range - this greatly improves your survivability at this stage of the fight. If you die partway through, you'll still have a few shadow scales - see if you can make a piece of shadow armor, and attempt the boss battle again.

Repeat these steps until you have full shadow armor. Equipping this full set and an ironskin potion makes the battle a walk in the park. At that point, you don't even need to artfully dodge his attacks; just sit there swinging your axe and reap the rewards.