Preparations for this mode's bosses
After a few sessions of exploration, you may think that you are ready to fight the first batches of bosses (unless you already accidentally met their requirement). What you could do to make things simpler, is to build an arena for that boss fight.
Quick Tip: DO NOT build your arenas really close to your base since almost all bosses go through walls and can murder your NPCs with relative ease.
Arena - The arena doesn't have to be a fancy. The most basic premise is to build a simple flat area where you don't have to worry about suddenly stopping due to terrain. A nice, long, flat land that has a few wooden platforms to aid you in gaining height easily in the early stages. First, resources. You need a lot of blocks to make this. Hopefully you stashed away those 999 pieces (or more) dirt blocks for this grand occasion. Some wood blocks that you could gather by chopping up trees and create Wood Platforms. Build the main area out of dirt and the insides would comprise of Wood Platforms. Below is a small scale version of what a bare-bones arena would look like. Obviously the actual one would be bigger but it wouldn't fit in one screen.
It is advisable to keep it simple since some bosses like Skeletron & Eater of Worlds have locations far from the starting point and would be easier if you get used to making arenas and build one near each of their locations. It would also help to make a small house with a bed so that you can respawn there if you die and avoid the long trek back.