Wyvern

Wyverns are long, white, oriental-dragon-like creatures which appear at certain heights on Hardmode (typically at or above the Floating Island level) and can even spawn directly above the start point of a map. Their appearance matches that of Haku in the anime movie Spirited Away. The wyvern spawn rate increases the higher up one gets.

The Wyvern attacks like a Devourer or Bone Serpent, making long, sweeping passes. Fighting them at high altitude and taking advantage of the lower gravity is useful for dodging, since they can do a lot of damage quite quickly. Weapons or Spells that strike a target multiple times (ex; Demon Scythe) are your best bet for fighting the Wyverns, as with any other worm. The Wyvern has a specific pattern; swoop in from where it spawns, and dive diagonally across the screen, homing in. If the Wyvern ever disappears off of your screen, expect it to come diving back down from the top of that part of your screen.

Fighting the Wyvern
Fighting Wyverns can be difficult as they deal respectable amounts of damage and are very fast. A wide variety of tactics are effective. The Clockwork Assault Rifle is extremely effective when coupled with the Rocket/Spectre Boots. With good armor and a few Ironskin Potions, a spear can also be quite effective. The Magical Harp is considered the best magic weapon to deal with the wyverns.

An experienced jumper can actually continually dodge it and kill it with something even as weak as a minishark if they dodge enough

If you are in an enclosed space like a house, spamming a weapon which bounces off walls can prove quite effective since the wyvern will fly right through the walls of the house to attack you.

It's also recommended you create a sky bridge at Space level, as you'll have low gravity and a slower descent. These advantages make it easier to face off the Wyvern.

If you can spare a gravitation and swiftness potion use them as soon as you find the wyvern. Jump down from the sky Island so the wyvern follows you. He should be pointed straight at you head first in pursuit. Use your strongest long range attack, and when he closes in on you, or reach the ground use the gravity potion to fly back up and repeat this process. With a Demon Scythe you only need to do this 2-3 times.

If you have a decent length of sky bridge (~500 - 1000 blocks long) and Hermes Boots or Spectre Boots, and the Demon Scythe: Similar to the above method, though instead of falling and having the Wyvern follow you down, you can run as fast as you can horizontally in one direction on your sky bridge. The Wyvern will start to catch up behind you - moving mostly horizontally. When he does, start firing the Scythe in front of you (the direction you are running). As you are running fast, and the scythes start slow, they will drop behind you and begin scoring hits, then blast forward following the Wyvern for a few more hits. You will take some damage if you dont jump out of the way when he catches you. He will then fly up and loops down for another attack. 2-4 runs like this usually finishes them off. I prepare sections along the sky bridge by killing Harpies with the scythe, then leaving the mana recharge stars sitting there for when a Wyvern shows up.

If you don't have a sky bridge, but you have decent armor(Mythril or higher is recommended), and can sacrifice a few hits, a good technique is to be hit once, then go slightly lower on the 1-block tower, then use a continuous weapon to hit the Wyvern multiple times. A Grappling hook and Healing Potions are required, as it will hit a large amount of damage.

Trivia

 * Although the name "wyvern" refers to a western dragon depicted as having two wings and two hind legs, but no arms or forelegs, Terrarian wyverns are shaped after eastern dragons originated in Chinese folklore, also know as 'lung dragons' in D&D. That means that the Terrarian wyvern doesn't have anything with the "normal" wyverns, and the name is quite incorrect. Because of their color, body shape and general style, Terrarian wyverns bear a close resemblance to several dragons from popular culture. Notable examples are:
 * Haku's true form, from the animated film Spirited Away.
 * Fuchur (known as Falkor in the English translation) from Michael Ende's "The Never Ending Story".
 * Given that Haku’s dragon form is depicted as having a tall green plume running the length of his body, absurdly longer curling fleshy whiskers, long sharp horns, and three jointed limbs, (none of which the wyvern possesses) but that Falkor is depicted as having 2 two jointed limbs, an all white body with mythril-colored scales on his back, a large smiling mouth, and large ears, (all of which the wyvern does posses) it seems likely that the wyvern is based on Falkor, and not Haku.
 * Also, when Falkor flies, his body moves up and down like a dolphin or running dog, but when Haku flies his body moves from side to side like a snakes. Given that terraria is two dimensional, the fact that the wyvern moves like Falkor and not Haku might be accidental or necessary, but it could also be another evidence that the Wyvern is more like Falkor than Haku.