Hardmode Bosses
Hardmode bosses are beefed up, mechanical versions of the easymode's bosses. The Twins are a stronger version of the Eye of Cthulhu but there is now two of them. The Destroyer is the mechanical version of the Eater of Worlds, and Skeletron Prime is, much like the name suggests, a prime version of Skeletron.
Most of the techniques used on the easymode counterpart bosses are still applicable to most of the new bosses only they have been buffed so it requires more from the player.
Most Equipment you obtain in easymode have hardmode counterparts. But killing them is still very doable with easymode weapons. Some players even manage to kill them without taking any damage!
Preparation for the hardmode bosses
Preparation for these bosses are roughly similar to what you have done previously. The rule still stands and is still do your best to make your gear out of the best hardmode ore which is Adamantite / Titanium ore.
In terms of arenas, It is a good idea to create a new one if your current one cannot be upgraded. Also, The Destroyer and Skeletron Prime no longer have a fixed place to spawn.
The Destroyer is no longer restricted to the corruption and will follow you throughout the world. The other bosses are relatively the same as their past limitations and same as before, if you haven't killed The Destroyer or The Twins by dawn, they will escape.
Skeletron Prime gains a one-hit kill move if you haven't killed him by dawn.
Your Arena should be expanded since these new enemies move way faster and have more complex moves to evade. So add a bit more height and length. A special addition to an arena if you are planning to use if to fight The Destroyer, is add some dirt blocks underneath the arena to allow it to "climb".
The Destroyer uses Worm AI that uses solid blocks so it can move through. If you don't add these blocks, time may be wasted with it just lounging around below.