Krampus

Krampus never spawns in the open world. He exists only inside the Frost Moon, the night event you start by using a Naughty Present, and he does not appear at the beginning of it either. The opening waves are the ones you are meant to walk through. He arrives once the night has escalated, in the stretch where the filler enemies stop being what kills you. The event belongs to the post-Plantera half of the game, so there is no reaching him early.

Killing one pushes the wave counter along by a real amount, more so on the harder difficulties, so he is worth prioritizing over the chaff around him. If your damage cannot put him down fast, this is roughly where a Frost Moon run stalls and the clock starts beating you instead of the enemies.

Krampus is a horned figure out of Alpine Christmas folklore who travels with Saint Nicholas and deals with the children who misbehaved, while Nicholas handles everyone else.