Wyvern

Wyverns live in Space and only start appearing once the world is in Hardmode. Altitude alone is not enough. The game also refuses to spawn one if a town NPC is nearby, or if the tile at your center has a safe background wall behind it, which is why a skybridge house full of NPCs is quiet and a bare platform is not. A Shadow Candle, held or placed, suspends both restrictions, so you can farm them from inside a built base rather than standing out in the open.

It is a worm, so it swims through solid blocks and its whole body follows the head's path. It will chase you down out of the sky all the way to ground level, but it will not go underground: drop below the surface and it turns away, then despawns once it has put enough distance between the two of you. Like every worm it ignores lava entirely.

The head has the lowest defense on the chain and deals roughly double the contact damage of everything behind it, which sets the shape of the whole engagement. You want to be hitting the head and you do not want to be standing in front of it. Anything that pierces or explodes multiplies its output across the segments: Jester's Arrow or Holy Arrow out of a repeater, the Onyx Blaster loaded with exploding bullets, the Nimbus Rod, the Medusa Head, and Life Drain, which pulls health out of several segments at a time. Thrown flails are the standout since 1.4: a well aimed Blue Moon or Sunfury can end one outright in Classic, and the Sunfury sets several segments burning in a single throw.

Early Hardmode is where a wyvern is genuinely dangerous, and the honest advice is to leave the sky alone until your gear catches up. When you do go, low gravity works in your favor, so fight high rather than near the ground. A Gravitation Potion plus horizontal movement while free falling puts you at close to its speed, and with movement buffs you can hold that position while it trails you, which turns the fight into target practice with a piercing weapon. Minecarts and the unicorn mount both outrun it if you would rather not fight at all.

Water Candle effects are stronger at high altitude, and on top of that a candle grants the wyvern an extra spawn roll of its own, close to doubling how often one shows up. That combination is the standard Soul of Flight farm. One thing to watch for: the head carries the drops, and it is possible to kill one whose head has drifted past the edge of the world, in which case the loot lands somewhere you cannot reach. Pull it back inward before you finish it off.

Despite the name, it is drawn as a Chinese loong rather than the two legged western wyvern, which is why it has four legs and no wings at all. Phantasm Dragons are described as the souls of wyverns raised by magic. Once Hardmode begins one may drift past in the background as scenery, and a wyvern shaped cloud can appear too; neither can hurt you.