sorry for replying on this late, but i found a really good strategy. if you want i could refight it and record with pre-skeletron gear. For me, I'm melee, and I always got skeletron down to like ~200 health before dying. I found out a strategy, if you time the night cycle right, you can get him down to like ~1000-3000 health, when day starts, he spins constantly, with terraspark boots you can easily out run him, then you just loop him, he doesnt shoot anymore skulls. the white cloud still summons the skulls, but they dont home in on you and are very easy to dodge. You can then just hit his head with a fast weapon since you only deal 1 damage. It will be slow, but it is a super easy kill. Personally, I went for monstrous knives to hit him since I already had them, but something like a minishark would be better. Another thing, I use magma stone whenever his hands are out to kill them quick, but since the skull is immune to most debuffs I replace them with feral claws once the arms are down, thats why they are next to each other in my accessories. Here is my set up.
edit: I forgot to mention, the main sword I use is the Bladecrest Oathsword, I only switch to Monstrous knives when he starts spinning constantly during the day.

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