Overview
The Rarify specialty converts Star Pieces into Rare Pokemetal, the most valuable crafting material in Pokemon Pokopia. Rare Pokemetal is required for crafting the Tidal Bell (summons Lugia), the Clear Bell (summons Ho-Oh), and for duplicating rare items with the 3D Printer.
Pokemon with Rarify
The primary Pokemon with this specialty is Porygon-Z.

Production Chain
Collect Stardust from Dream Islands (found as ground pickups; usually takes about 2 trips to gather 99).
Craft a Star Piece at a Workbench: 99 Stardust = 1 Star Piece. The recipe is learned automatically the first time you interact with Stardust.
Give the Star Piece to Porygon-Z. It processes the Star Piece over time into Rare Pokemetal.
Collect the Rare Pokemetal once processing is complete.
Tips
Visit Dream Islands daily to stockpile Stardust.
Star Pieces can also be gifted to visiting Pokemon on other players' islands to receive rewards.
Star Pieces have a trade value of 500 (750 if the Pokemon considers it a favorite).
Rare Pokemetal can also drop at a low rate from Pokemetal Fragment blocks when broken with Rock Smash.