Pre-Skeletron
Now that you have your starting gear, we can start killing bosses. The first of which, you may have already encountered if an event has happened in your world. That boss is the King Slime.
King Slime
At the core, he is simply a larger version of the slimes that have already been harrasing you. Except he hits harder, summons smaller slimes, and teleports to you if your ever to far away. Spawning the boss requires a feature that you may have come across depending on your exploration.
Crafting Boss Summons
To craft a majority of boss summons you need a demon altar, which can be found in your worlds corresponding evil biome. These demon altars will become useful in hardmode, so keep in mind where a few are located.
The Slime Crown
Crafting the first summoning item is rather easy. It only requires 5 of your world's tier 4 ore and 1 ruby. Fighting the king slime is rather easy with Hermes boots, keep your distance and you will be fine
Suspicious Looking Eye
The next boss is also rather easy to summon, but it can be difficult using Melee. If you saw the text "An evil presence is watching you" a bit before night in your world. Then the Eye of Cthulhu has spawned before. It's recommended that you build an arena to fight this eye. If you take 6 lenses (obtained from the demon and wandering eyes at night), to a demon altar you can create a suspicious-looking eye. Using this eye anytime at night will spawn the eye of Cthulhu.
Fighting the eye
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The eye will charge at you slowly, spawning servants of Cthulhu(they look exactly like the suspicious looking eye summon item) that will also be charging at you. Upon getting to half health, the boss will transition into phase 2.
Fighting the eye
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In phase 2, his charges become faster and more aggressive, spawning a larger amount of servants. After you manage to beat this boss, if you're in expert mode as I suggested, you will get your first upgrade. That being the Shield of Cthulhu, allowing you to dash horizontally, giving you access to better movement. It also gives you demonite, which you can use to craft Light's bane(the second image above), a small damage upgrade for the next fight.
Fighting the eye
With this new item, you can now go and fight the "evil biome boss" of your world. That being either the Eater of Worlds or the Brain of Cthulhu. This guide will be going into the Eater of Worlds as it's part of the evil biome I suggested you chose at the start. Summoning this boss can go 1 of two ways, crafting an item, or destroying orbs inside of the evil biome. So in case we run out of orbs, it's time you build some NPC housing so the Demolitionist can move in. As the explosives from him are needed.
Worm Food
While you wait on that, you can collect mushrooms from the evil biome, and collect rotten chunksfrom the enemies there. Using the mushrooms at a placed bottle, you can craft vile powder, combining the vile powder with rotten chunks you can make Worm Food, which is used to summon the boss.
Shadow Orbs
Once the Demolitionist spawns, you can buy dynamite from him to blow up orbs in the depths of the evil biome. Blowing up three of these orbs will also spawn the boss.
Shadow Orbs
The boss fight itself is rather simple, do not get hit by the face of the boss, and if needed run into its body to avoid it. Once you begin to destroy segments of the worm, it will become harder to avoid the multiplying faces. At this point, you would ram into them with your Shield and hopefully time it right to negate the damage. After beating this worm, it is time for a lot of upgrades, and the two hardest bosses of pre-hard mode. Skeletron, and the Wall of Flesh.