The Twins

The Twins are a hardmode version of the Eye of Cthulhu boss. They can be summoned at night with the Mechanical Eye or just at a Blood Moon.

Both eyes have their own individual life meter and the ability to teleport around. The red one, Retinazer, fires purple eye lasers while hovering above and to one side of the player. The green one, Spazmatism, shoots a flamethrower like stream that appears to be formed of Cursed Flames. It keeps a set distance on one side of the screen, level to the player. Both alterante between their signature attacks and a charging attack, much like EoC. Note that Retinazer's charge dash is faster and covers a bit more distance than Spazmatism's charge dash.

Just like the Eye of Cthulhu, when they have been hit for half of their health, they change. Retinazer becomes a mechanical eye with a laser turret in its pupil, while Spazmatism becomes a mechanical mouth. After changing, Retinazer will start firing lasers more aggressively, and his lasers will be red death lasers that do more damage. It alternates between chasing the player with periodic fire and slowing down for rapid-fire. Spazmatism will begin chasing the players faster and constantly spewing Cursed Flames from its mouth. The Cursed Flames can inflict the Cursed Inferno debuff upon players. It alternates its flamethrowing attack with a much more aggressive charge dash that is both faster and covers quite a distance.

Tactics
When fighting The Twins, it is perhaps best to focus on taking one down as quickly as possible rather than spreading damage between them. Each part has its own life gauge and eliminating one makes killing the other much easier.

Spazmatism is probably the easiest to kill first as it chases the player at the same level. Retinazer chases the player above the player, necessitating leading adjustments if using ranged weapons (which you'll probably use as both hit for significant damage in melee.) Just aim parallel to the ground and you can easily pump Spazmatism with arrows or shots.

A wide-open, flat area is recommended for the fight for ease of evasion. If the ground is level enough to run across, it's possible to just kite the bosses with bow-/gunfire by running and simply shooting them as they give chase. Mobility is key. Rocket Boots, Spectre Boots, Angel Wings and/or Demon Wings are recommended.

If possible, a Megashark with Crystal Bullets make this a much easier fight (along with a ranged-type armor set). You need to kill The Destroyer first to get the Megashark, however.

Trivia

 * Retinazer's name is a portmanteau of retina, a part of the eye, and lazer. Spazmatism's name is a portmanteau of astigmatism, an eye disorder, and spazm, meaning to twitch uncontrollably.
 * The twins will disappear if the player(s) are too far away.