The First Bosses
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. He is just a larger version of the slimes that you have already been fighting, except he is much harder and much faster. Spawning him requires the slime crown, which can be crafted with 20 gel, and a slime crown (5 of your world's tier 4 ore and 1 ruby). Combining all of these items at a demon altar will give you your slime crown. He can be spawned at any time and is great to practice your movement before we get to harder bosses. Speaking of harder bosses the next one is another that you might have seen before. 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. 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. 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, a small damage upgrade for the next fight.
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. 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. 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. 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.
Image References
King Slime
Slime Crown
Slime Crown Materials
Demon Altar
Eye of Cthulhu
Suspicious Looking Eye
Eye of Cthulhu in second phase
The Shield of Cthulhu
Light's Bane
Eater of Worlds
Shadow Orb used to spawn the Eater of Worlds
Tall NPC house
Worm Food
Face of the Eater of Worlds