Terraria (UP)

PRE-HARD MODE BOSSES

King Slime - Summoned with Slime Crown
Eye of Cthulu - Summoned with Suspicious Looking Eye at night ONLY
Eater of Worlds - Summoned with Worm Food in Corruption Biome or by destroying 3 Shadow Orbs
Skeletron - Summoned by equipping Clothier Doll in an accessory slot and slaying the Clothier at night or by going to Old Man in front of the Dungeon at night to lift his curse
Brain of Cthulu - Summoned with Bloody Spine in Crimson Biome or by destroying 3 Demon Hearts
Queen Bee - Summoned with Abeemination in Jungle Biome or by destroying the Baby in the Hive in the Underground Jungle Biome
Wall of Flesh - Summoned by sacrificing (burn in lava) a Guide Doll in the Underworld Biome; this unlocks Hard Mode and gives an achievement:

Check it for tricks on killing this boss.

HARD MODE BOSSES

The Twins (Retinazer and Spasmatism) - Summoned with Mechanical Eye at night ONLY (upgraded form of Eye of Cthulu)
The Destroyer - Summoned with Mechanical Worm at night ONLY (upgraded form of Eater of Worlds)
Skeletron Prime - Summoned with Mechanical Skull at night ONLY (upgraded form of Skeletron)
Ocram - Summoned with Suspicious Looking Skull at night ONLY [BOSS HAS BEEN REMOVED]
Plantera - Must Destroy one of the Mechanical Bosses (Twins, Destroyer and Skeletron Prime) to get the message "The Jungle Grows restless." This will spawn a Plantera bulb in the Underground Jungle, which you must destroy with a pickaxe. They are glowing pink bulbs. You can continue killing the mechanical bosses to spawn more bulbs.
Golem - Summoned by using Lihzahrd Power Cell at Lihzahrd Altar (found in Jungle Temple and may be relocated); need key from Plantera to get in Temple

SUMMON ITEM RECIPES

Slime Crown - Gold/Platinum Crown and 99 Gel at Demon/Crimson Altar
Suspicious Looking Eye - 6 Lens at Demon/Crimson Altar
Bloody Spine - 15 Vertebrae at Demon/Crimson Altar
Worm Food - 30 Vile Powders and 15 Rotten Chunks at Demon/Crimson Altar
Clothier Voodoo Doll - rare drop from Angry Bones or Dark Casters in Dungeon
Guide Voodoo Doll - dropped by Voodoo Demons in the Underworld
Abeemination - 5 Honey blocks, 1 Stinger, 1 Bottled Honey, 5 Hives, 5 Crispy Honey Blocks, and 5 Obsidian at Demon/Crimson Altar
Mechanical Eye - 3 lens, 5 Lead/Iron bars, 5 Copper bars, 7 Soul of Light at Mythril/Orichalum Anvil
Mechanical Skull - 30 Bones, 5 Lead/Iron bars, 5 Copper bars, 5 Soul of Night, 5 Soul of Light at Mythril/Orichalum Anvil
Mechanical Worm - 6 Rotten Chunks/Vertebrae, 6 Soul of Night, 5 Lead/Iron Bars at Mythril/Orichalcum Anvil (thanks ThaDevilzHand)
Suspicious Looking Skull - 1 Mechanical Skull, 2 Mechanical Eyes, 10 Adamantite bars, 5 Soul of Light, 5 Soul of Night at Mythril/Orichalum Anvil [BOSS HAS BEEN REMOVED]
Lihzahrd Power Cell - found in Jungle Temple from Lihzahrds or in chests

TIPS/TRICKS
Check out the Terraria Wiki for tricks for each boss
It is recommended to BUILD AN ARENA to fight them in that is close to your home/bed for quick respawning and getting back in the fray.
It is also easiest to kill bosses with other friends in a co-op setting.
The duplicating method is easiest for obtaining the summon items or ingredients to craft them, or any weapons/armor.
Check the Leaderboards to make sure each boss has been killed and recorded, and note that Queen Bee, Brain of Cthulu, Plantera and Golem are NOT LISTED in the Leaderboards.
Note that Duke Fishron, the Pumpkin Moon, Frost Moon, or Lunar Event creatures and bosses do not count for the achievement!
Feel free to add a comment and I will credit you in the solution. :)

NOTE: if boosting, as long as you are present for the death of ANY boss and get the message "(Boss Name) has been defeated" it counts for you on the Leaderboards and for the achievement. -- thanks to iiTz xFIREL0RDx for pointing this out.

Pre-Hardmode Bosses

Eye of cthulhu

King slime

Eater of souls

Brain of cthulhu

Queen bee

Skeletron

Wall of flash

Hard mode Bosses

The twins

The destroyer

Skeletron prime

Plantera

Golem

Duke fishron

Lunatic cultist

Moon Lord

The queen slime, empress of light and deerclops, do not count for The achievement

kill bosses on multiplayer sessions only counts for the host.

The other guides are good but alas I was playing solo and even with duping materials with a second account I was still under-geared and struggling to do good damage to hard mode bosses, especially the twins and skeletron prime.

Fear not I found an easy way to cheese them

This requires you to have the pirate captain NPC, for him to show up you need to have a pirate invasion and, the odds of this occurring randomly are low enough so we need to make it happen with a pirate map, grab a water candle from the dungeon or a battle potion will do so enemies spawn more and go to the far left/right of the map to the ocean and place the candle or use potion and kill fish till you get the map, then use it and beat the pirates (120 i think)

Once the npc shows up buy cannons and cannon balls from him , cannon costs 25 gold so might be wise to either dupe gold or the cannon and ammo with a second account .

Build an arena about the size of your screen , basically a box to fight in and line the bottom of it with cannons pointing up, add some heart lanterns and camp fires too. Summon the boss and hit X to use as many buff potions as you have in your inventory with a single press of a button and have the cannon ball ammo selected , then it's a matter or strafing left to right keeping an eye on your health and holding RT you use the cannons to blast the bosses . Cannon balls do 300 damage each so they should rip the boss to shreds, I don't think there is anything in the game at that point that can do that kind of damage that early on in hard mode ?

Here is a video of me killing a boss with this set up

IMPORTANT: Make sure your cursor / pointer is on auto and not manual when firing cannons other wise you will have to aim at each cannot to fire it. When it's on auto you can just move left and right holding RT to fire them as you pass.