What is the best way to kill Skeletron Prime in Terraria?
Before Skeletron Prime
Skeletron Prime isn't the easiest of all the three mechanical versions of bosses. Saying if he is the hardest or if The Twins is the hardest is subjective, but it's common sense that a proper arena make the battle against Destroyer easier than the others.
Break a few altars, at least 6, so that a minimum amount of ores are spread across your world. After that, try getting a third-grade ore armor. With a grappling hook, a small cave arena with proper healing items, and you're good to go.
After killing him, you can make a proper Weapon with Hallowed Bars if you couldn't get a good one.
A wing is highly recommended for the other 3 bosses. To make a wing, there are many basic recipes, but the common material is the Soul of Flight, a 100% drop from wyvern, that can spawn high on the sky and floating islands.
Arena
The arena can be built with a few platforms, 5 is enough, on the air, so that the bomb goes trough all platforms to the ground and doesn't hit you. Statues with timers, Heart Lantern and campfire for passive health generation. If you are not playing alone, the players that is not aggroing the boss can take quick jumps on a honey pool.
Gear
The armor that you used to defeat Destroyer is good enough. If you want a Hallowed set by farming Destroyer, would be good as well. As melee, don't even dare using swords without projectiles. The best weapon I can think of is the Bananarang, having at least 5 of them, since the number of it you have equipped is the amount of boomerangs that can be had active on the screen(you will probably get 2 or 3 the first time you get, so kill a few more clowns to get to 5).
As ranged, a Hallowed Repeater or a Megashark (using the Souls from Destroyer) is good enough.
As magic, the best spell against him would be Magnet Sphere, but this would be hard to get since Dungeon in Hard Mode is almost end game content. Meteor Staff would be the second in place for this battle, since he is flying, it would shouldn't be a problem to hit him. Since the nerf on the mana potions I highly recommend magic handcuffs and star statue.
The Battle
For the battle, there's not much you can do to avoid damage from the laser arm, just make sure to have good speed, your wings, healing and buff potions, and go for it. Focus on the the arms that actually shoot, and keep your distance to avoid contact damage, it's the biggest source of damage of the boss.
Here's what I did for my first win against him.
Hung out in the hallow and underground hallow to get a) Pixie dust b) Unicorn Horns c) Souls of light
Made a few hallowed mimics to kill (chest + key of light - made from souls of light). Until I got a Daedulus bow.
Made holy arrows from the pixie dust and unicorn horns. (I made about 1K, but that was overkill)
Horizontal sky arena from two parallel platforms spaced a double jump apart. Quite long. Put a heart statue at one end and heart lanterns and camp fires placed along it.
Summon and rain holy arrows down on him.
Switched to different weapon when only head was left (I used yoyo but use whatever floats your boat.)
It was pretty safe and pretty quick. Just run back to the heart statue to get healed.
Used the same arena / strategy for all three mechanical bosses, worked pretty well in all cases.
Wasn't using anything amazing something like - Oraculum armor, obsidian shield, some basic wings (not really needed) and lightning boots - not even all reforged.