Wandering Eye

Surface, after dark, and only once the world has gone into Hardmode. Nothing summons them and no item is involved. They simply fly in as part of the night. New moon nights are the exception worth planning around, since the numbers climb sharply, so if you want the banner or the kite, wait for one instead of grinding ordinary nights. When the sun comes up the survivors turn and run, and they vanish the moment they leave your screen, so anything you want off them has to die before dawn.

Picture a Demon Eye scaled up. It floats at you in a rough line and clatters off terrain rather than steering around it, so walls and ceilings send it ricocheting in directions neither of you planned. It also takes knockback badly, which means any weapon with weight behind it keeps one at arm's length indefinitely while you keep hitting.

Drop it under half health and the pupil tears off, leaving an open mouth of teeth the way the Eye of Cthulhu opens up. It gets faster and nothing else changes: no new attack, no new pattern, just the same approach arriving sooner. That only matters if your plan was to outrun it, which it usually is not, given how far a solid hit sends one.