One of the services you can access inside the Pocket Castle is Papi's smithy. A total of four tiers of equipment can be bought here: iron, golden, mithril and crystal. She starts out with only iron weapons and armor, the higher tiers can be unlocked through this quest.
Similarly to Vanilla's inventory, Papi's stock gets reset when you start a New Game+. However, you don't need to go through the process of recruiting her again, unlike the vampire girl.
The only prerequisite of this quest is Papi being a companion. She needs to be in the party when you speak with the blacksmiths.
- Get the Gold Ore from Midas Abandoned Mine
- Talk to the Midas Village blacksmith, he'll agree to teach your dragon in exchange for a Stone of Chaos
- Go get the stone (they're dropped by monsters from the first Tartarus)
- Talk to the gold smith again and give him the stone (Unlocks golden equipment, gives Papi the blacksmith achievement)
- Advance the main quest to the point where you fight Page 65537
- After defeating her go talk to the pope
- Go to the Amos Mountains and get the mithril ore
- Talk to the San Ilia blacksmith, who'll say that you need strong faith to forge mithril
- Recruit Sofia, Christie or Rosary (Sister Lamia, Succubus Nun and Slug Nun respectively)
- Get one of them to 10 affection and talk to them in the castle to get the Proof of Faith
- Talk to the mithril smith again and show him your Proof (Unlocks mithril equipment)
- Go pay a visit to the Lizard Boss in the Salon Mine, after defeating her you can take the Crystal behind her throne
- Go to Salon and take a look at the blacksmith's wares
- Talk to her again and she'll agree to teach Papi in exchange for Star Sand
- Go get it from one of the chests at Salon Hill
- Deliver the sand to the crystal smith (Unlocks crystal equipment, gives First class blacksmith achievement)