How to kill Eye of Cthulhu

The eye of Cthulhu is a boss in Terraria that can be summoned by suspicious looking eye. It has a basic health of 2800 in the first phase and 1400 in the second phase. It looks a lot like the Demon eye. It can be summoned with suspicious looking eye that can be made at a demon altar using 6 lenses. Trying to summon it twice at the same time will result in instant death as with all the other bosses. The suspicious looking eye can also be found in some chests. It also has a random chance to summon itself(33.33%) if it has not been summoned before. While playing you will recieve a message: "You feel an evil presence watching you.." to indicate the eye of Cthulhu will awaken in a few minutes.

Early Game Strategy:
The Terraria wiki suggests the following method!:

Preparation is key when going up against what's likely to be your 1st boss (or for any other boss in this game). Since the Eye of Cthulhu can only summon itself if your max HP is 200 or more, you can delay its arrival by holding onto any Life Crystals that'll increase your max HP to 200 or more until you feel that you're ready. That way, you'll be able to get good equipment, you should at least have Iron Arm o r or better, an Iron Broadsword or better, and, most importantly, some sort of ranged weapon, such as Shuriken, Throwing Knives, or a bow (preferably Iron or better) with Flaming Arrows. Also, bring along any Lesser Healing Potions in case you need to heal.

The following consumables may also be of some help:give sloppy toppy After doing all of this you can summon him, while he flies above you, you can throw him with shurikens, knives or shoot with your arrows. If he comes close to you attack with your melee weapon like the sword but do not stand still as he will kill you. Move and jump dodging his attacks. The other method is to do exactly the same but on a sky bridge as with wyvern.
 * Ironskin Potion: This will increase your defense by 8 for 5 minutes, allowing you to take up to 4 less damage from the Eye of Cthulhu's attacks.
 * Thorns Potion: For 2 minutes, enemies will take half of the damage that you take. This can make the battle go a bit quicker, though you'll probably want to try to avoid the Eye's attacks, especially during phase 2, where they can do a whopping 30 damage. It can cause the Servants of Cthulhu to die instantly on contact with you, though you shouldn't let them touch you anyways, as they'll deal 23 damage.
 * Archery Potion: For 4 minutes, the damage dealt by your bow & arrow increases by 20%.
 * Regeneration Potion: For 2 minutes, your health regeneration is augmented, allowing you to recover more lost health in a faster period of time.

Late Game Strategy:
Use your Starfury, as after the release of 1.2 it no longer uses mana.

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Hardmode/Late Pre-Hardmode Strategy:
If your armor is strong enough, you can easily defeat 3+ eyes in a single night. Simple pull out a trusty flare gun, and go wild. Wait as long as you can before spawning another Eye in, for there is a limited amount of flares allowed in one world.