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Polterpup first appears in Gloomy Manor, where he is playing in the Mudroom Exterior and discovers an Amethyst after digging around the ground. While briefly playing with it, Polterpup winds up getting the Amethyst stuck in a tree, after which he leaves the Manor.
Later, Polterpup appears in Haunted Towers during the mission Pool Party. After Luigi finds the special key in the pool, Polterpup runs up and playfully takes away the key. However, unlike his fellow ghosts, the absence of the Dark Moon's pacifying effects renders Polterpup nonviolent and mischievous, rather than hostile and aggressive. This is evident when Luigi briefly plays with him and, in the event Luigi loses all of his Heart Points, Polterpup will even lick him back to health as long as Luigi has a Gold Bone.
After Polterpup steals the special key, Luigi has no choice but to chase after him in the mission Doggone Key to retrieve the key. Luigi finally catches him, but before he can store him in the Ghost Container, Polterpup manages to escape from the Poltergust 5000 and flees yet again. It is at this point that Professor E. Gadd surmises that Polterpup is lonely and is looking for someone to play with, even if his attempts to do so unintentionally cause trouble for Luigi.
Polterpup returns in the Old Clockworks during the mission Play Catch, where he steals the second Clock Hand from a group of Greenies. Luigi has to chase after him yet again before finally catching him in the Poltergust 5000. Despite this, Polterpup manages to escape yet again before he can be stored away. Polterpup returns yet again in the Treacherous Mansion during the mission Front-Door Key. Just before Luigi can go through the front door, Polterpup jumps out of the keyhole and knocks the key out of Luigi's hand. He flees to the basement, causing a long and paranormal chase through the odd rooms. This time, Polterpup is able to be properly kept within the Ghost Container thanks to E. Gadd's repairs.
Following King Boo's defeat and the restoration of the Dark Moon, Polterpup and his fellow ghosts are finally released from the Ghost Container. Upon being released, he unhappily approaches Luigi in acknowledgement of having caused his fair share of trouble during the absence of the Dark Moon. However, Luigi nevertheless cheers him up, much to Polterpup's delight. After Polterpup takes a celebratory photograph alongside Luigi, Mario, E. Gadd, the Toad Assistants and a few of his fellow ghosts, he is adopted by Luigi and accompanies him back to his home as his new pet.
Ghost Container description
I haven't come up with a name for this mischievous and adorable Polterpup yet. He's caused us a whole mess of trouble, but I think the playful tyke just wants someone to take him in.