Gotcha! - Defeat a boss after you've died. (through poison, venom, etc)
Who needs legs anyways? - Defeat a boss without using the basic movement keys. (W, A, S, D, space, basically by using just a hook)
Look ma, no hands! - Defeat a boss without using any weapons. (through minions, traps, etc)
Ophthalmology - Have Eye of Cthulhu and the Twins alive at the same time.
Running Riot - Defeat 7≥ bosses in 1 night.
Chutes are for cowards - Fall 1000≥ ft. without any accessories equipped, land on solid ground (no liquid or cobwebs to obstruct the fall at any point) and survive. (you would have to use a hook on the ground just before touching it to survive)
Full House - Have every single NPC moved in. (possibly excluding santa)
Stop punching yourself! - Defeat the Golem with only the use of the weapon "Golem Fist".
Cannibalism - Kill a piranha with only the use of the weapon "Piranha Gun".
Anarchy - Defeat the Queen Bee with only the use of the weapon "Bee Gun".
Have a taste of your own medicine - Defeat Duke Fishron with only the use of the weapon "Flairon".
Rage Quit - Save & exit within ≤15 seconds of dying.
Climax - Reach maximum health and mana. (excluding health obtained from the lifeforce potion and mana obtained from accessories and armor)
Shinobi - Kill any mob with a shuriken while the ninja vanity set and the accessory "Master Ninja Gear" are equipped.
What just happened? - Use the teleportation potion for the first time.
Unlucky - Reforge the same item 50≥ times.
That's cheating! - Get killed by Skeletron while it's day.
You monster - Kill 5≥ different critters at least once.
Flawless Battle - Defeat Duke Fishron without taking a single hit.
Parenticide - Defeat the Twins with only the use of the weapon "Optic Staff".
Coward - Teleport while fighting the Wall of Flesh.
Kamikaze - Defeat a boss and kill yourself with the same grenade.
Close Call - Dodge a hit which would've killed you if not dodged. (with the "Black Belt" or "Master Ninja Gear")
You're coming down with me! - Defeat a boss with the turtle armor's set bonus who also kills you.
Achievements for when the messages "The jungle grows restless..." and "Screams are echoing from the dungeon" appear would also be a good idea in my opinion.