Pedguin's Hood

Ordinary penguins carry nothing. You need the corrupted forms, Corrupt Penguin in a corruption world and Vicious Penguin in a crimson one, and those only exist while a Blood Moon has turned the normal ones. Chasing the set by wandering the tundra is slow for that reason: you are waiting on the right night and on enough penguins happening to be nearby.

The reliable answer is to build the spawn yourself. Wire one or more Penguin Statues to a timer, park yourself next to them for a Blood Moon and kill everything they push out. Statue spawns get converted the same way wild ones do, so the drop rolls normally and you get far more attempts per night than open terrain will ever give you. Each of the three pieces rolls on its own, so plan on finishing the outfit across several Blood Moons rather than one long session.

Pedguin is a Terraria streamer, and delivering his outfit through penguins is the whole joke. The tooltip is a rewrite of the line the developer costumes carry, aimed at streamers instead of staff. He is one of a very small group of creators with an item in the game, alongside a pair of sunglasses and a couch, and those three are the only pre Hardmode items sitting at that particular rarity.