The Twins
The Twins is the hardmode version of the Eye of Cthulhu only now, there's two of them and are highly aggressive right off the bat. The one with the red iris is Retinazer which fires lasers at the player. The one with the green iris is Spazmatism which shoots green fireballs. It is recommended that you use an Arena that is really long and with sufficient height.
Similar to the Eye of Cthulhu, damaging one of them too much will force it to transform. So simply focus on one eye first as you do NOT want to fight both of them in their transformed state together. Since Retinazer is easier to dodge than Spazmatism, focus on Spazmatism first.
Spazmatism's first stage shoots simple green fireballs that can burn you if you are hit. They are dodgeable by running backward and running OR, jumping circles around the eye. The important thing to do, as in most of these boss fights, keep moving to make yourself a harder target.
When it reaches a quarter of its health, it will enter its second, more vicious form. Its green fireballs will now shoot a constant green flamthrower. In this mode, It is recommended to circle around it continuously to keep the flames off of you. Keep on it until it Spazmatism is no more.
Quick Tip: Since Health Potions have a cooldown, and there are no enemies to spawn hearts, use a potion when your HP needs healing. Don't wait till you absolutely need it.
Retinazer's first stage shoots lasers and just stays further from you due to its chosen weaponry. It is far more slower than its aggressive partner. He is much more of a pain to a melee user since it tries to keep its distance so just stick with ranged. Upon damaging it enough times, it will transform and gain a more powerful laser in every way. It will sometimes spin and scatter shot lasers around the place or it will also sometimes do simple charge attacks that pale in comparison to its partner's charges. Hang on in there and stick with the strategy until both of them are dead.