Skeletron Prime
Skeletron Prime is the mechanical hardmode version of Skeletron. He generally has the same moves as skeletron except instead of two limbs to watch out for, you now have four limbs to watch out for! Effectively doubling its attack capability much like The Twins are a far more capable form than the Eye of Cthulhu. Its limbs will have particular characteristics unique to each of them. Below are a short description of what each does.
Prime Cannon
The Prime Cannon shoots bombs at the player only that these bombs only detonate on contact with normal blocks. The best workaround to effectively nullify this part's capability is an Arena that has a long and high walkway of platforms. Since the bombs only detonate on contact with solid blocks, it goes through platforms.
Prime Laser
The Prime Laser constantly shoots similar to what The Twins' Retinazer and The Destroyer uses. This limb doesn't move around too much so if you check its location, you will know where the general direction and path will go.
Prime Saw
The Prime Saw is one of the two weapons that resemble normal mode's Skeletrons attack patterns by being a melee attack. It usually waits around the player to suddenly swipe the player. Just keep an eye on it and keep moving.
Prime Vice
The Prime Vice is the most erratic of the melee moves that Skeletron Prime has. It will thrust at the player occasionally. Opposed to its name, the vice doesn't grab and hold player. It works in tandem with the Prime Saw in the goal of pressuring the player's move space.
Skeletron Prime (Head)
Skeletron Prime's head is the most docile amongst its limbs. Its only attack is the headspin BUT! unlike its easymode counterpart, it GAINS double defense when it spins. So attacking it while it spins is not a good idea especially if your weapons consume ammo.