Guide:The Twins strategies

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.

However, even though Spazmatism is easier to hit initially, his second form may be harder to fight for some due to its constant chasing of the players with both it's flamethrower-like attack and its charging attack which is the most damaging move The Twins have. As such, choosing to eliminate Retinazer first may prove to be the more beneficial option as one may have an easier time avoiding Spazmatism's later attacks if Retinazer is already gone.

In either case, whichever a player decides to eliminate first, it pays to make sure damage is concentrated on one of the bosses as much as possible. Avoid doing damage to both to the point that both transform into their second phases. Killing one is much easier when only one is in it's second mode and the other is still in its first form. The first forms are more predictable and tame compared to the second forms.

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.

Note that once one of them is killed, regular mobs can now spawn during the fight with the other half.

Equipment
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.

A Shotgun isn't advisable due to the refire rate being so slow and that to maximize damage, you need to be right next to enemies to ensure many bullet in the spread hit. A Clockwork Assault Rifle may work as it's comparable to the Megashark and possible to get sooner via Wall of Flesh farming. (You trade some power and overall damage over time for endurance, as you get 3 times the ammo usage, guaranteed. This compared to the Megashark slightly higher damage, faster firing rate, but only effective doubling of ammo with its 50% chance to not use ammo.)

Rocket Boots, Spectre Boots, Angel Wings and/or Demon Wings are recommended for increased mobility. If no Angel/Demon Wings are available, be sure to equip a Lucky Horseshoe or an Obsidian Horseshoe to negate fall damage from the heights you can reach. Or use a Featherfall Potion.

If farming the Wall of Flesh, a Ranger Emblem helps speed up the process of whittling away their health with its +15% ranged damage bonus.

If money is no problem and a player has rescued the Goblin Tinkerer, upgraded accessories and weapons can help immensely. Cost can be relatively cheap or expensive, depending on the item being upgraded and some luck. Increased movement speed or damage bonuses on accessories are perhaps the best. Speed eases evasion while damage allows faster kills. (Up to +20% bonus if all five accessories have bonuses of +4% of the same type.)

dart193's strategy
Build a platfrom 1000 blocks long(4 stacks of dirt is what you need). Gather adamantite armor. Have as much defense in accessoires as possbie.

Now the most important - potions.

1. Ironskin potion. The more defence the better.

2. Swiftness potion. Highly recommended, a must if no hermes boots.

3. Regeneration potion. Lasers and cursed flames are not that hard to avoid, but when Retinazer enters the second phase, you will receive a lot of damage, so your health must be replenished.

4. Gravity potion. Spazmatizm will move much faster than you when charging at you in second phase. It renders dodging almost impossible without flying. However, if you have wings, then this potion is not that useful.

The weapon I chose was megashark and crystal bullets. You will be running a lot and avoiding shots, so no time for aiming. Crystal bullet will deal massive damage as when the eye charges, as it will charge into every shard.

The battle
Start running as soon as possible. The run left, right, left right on your platform. This will negate their charges as they are just slightly faster than you so you should be far away when they charges at you. Concentrate a fire on Retinazer. There are two reasons: first one is that his lazers are harder to avoid than flames, second - the second phase of Spazmatizm is dodging most the time so you will want to have less obstacles including the Retinazer.

Killing Retinazer is not hard, even when he goes second phase. Just jump a lot or fly.

When done with Reti, shoot Spazmatizm. When he goes second phase... well, you die, if you are not prepared. He will do a line of flames so long that you have to keep it almost out of screen. When he charges, he is ... 3-4 times faster than you. So you have to fly or jump very much. BUT when he is flamethrowing, he is slower than you, so the strategy is: shoot him when he is shooting you, avoid him when he is charging you.

The battle is not that hard even with not big defence, you only need to fly a lot.

Small advice: if you are running low on HP, try to get to the Nurse and heal. This saved me a lot.

Necrodoom's strategy
While at first the bosses may seem scary and hard, some few preparations will make them easy. spazmatizm is the melee and cursed flame eye, while retinazer is the laser eye. the thing that makes this boss so predictable is that spazmatizm stays on the X axe, while retinazer stays on Y axis, which means you can easily block an axis and you can solo each eye at a time.

The Arena
A long section of 2 rows of wood platforms, and a ceiling, and a small pit section, 50 blocks wide.

Items To Take
The eyes are very fast, so hermes boots along with swiftness potions are needed to outrun them so you wont take damage. Take your ranged weapon of choice to fight the eyes.

The Battle
Right as the battle starts, run along the long platform and shoot spazmatizm, drop and jump on the 2 platforms to avoid the missles. retinazer will harmlessly attempt to fire at you, but the ceiling will block it. When they charge toward you, use your swiftness potion and keep running and shooting along the platform. When spazmatizm changes form, keep the swiftness effect on at all times so you can outrun spazmatizm while he shoots you. Once he goes down, drop into the pit section so retinazer goes though the ceiling, and run back and forth on the floor, shooting him. Even when he goes second form he shouldnt be able to hit you unless he charges at you while you are at a corner if you keep drinking swiftness potions, so you pretty much won at this point.

Icke's strategy
Why bother making a huge fighting arena if the best arena is already there: the sky. This strategy will let you kill the twins with medium level equipment.

The Arena
The fastest way to change height is by falling, so the arena will be the sky. Also while you are running away from those eyes you don't want to turn around because you reached the end of the arena. Therefore make a large map for the fighting arena. It is possible with a small/medium map too, but you have to be careful not to get too high, because at the top of the map you will fall slower, making it impossible to evade attacks.

Equipment

 * Armor: Of course you should take the best armor you can get, but if you have some good defense accessories molten armor should do. If you use cobalt armor take the helmet and for adamantite or better helmet and mask are both fine.
 * Accessories: As you will use gravitation potions items like wings/rocket boots/shiny red balloon/cloud in a bottle aren't needed. You may want to equip a lucky horse shoe, to make sure you don't suddenly hit a floating island causing you to die. An obsidian shield/cobalt shield is needed and a ranger emblem is going to help a lot in case of low level armor. Aside from that take an aglet/anklet of the wind for extra speed and fill the remaining accessory slots with defense increasing accessories.
 * Potions: Iron skin is a must have when you use low level armor and could prove useful for higher level armor as well. Regeneration potions and (greater) healing potions are needed to keep you healthy. As the whole idea is not to get hit a swiftness potion is a must have and last of all enough gravitation potions to stay in the air all night.
 * Weapon: a starcannon could be easy, but it will require a lot of stars. Therefore a clockwork assault rifle may be a better choice, as it will almost do enough damage as well. As bullets you should take crystal bullets(3 stacks should be enough if you can aim well.) Minishark may work too but I haven't tested that. In that case you may need more amo.

The Fight
It will properly only take half the night to kill the twins, but nevertheless you should start the fight at dawn. Start by drinking all potions and get up in the air and summon the twins. The best way is not to turn around, so just keep flying in one direction for the whole fight. Also make sure you don't go to high, as the low gravity will make it impossible to evade the incoming attacks. Focus all fire on Retinazer so that he dies before Spazmatism goes to his second form.