Once you have 15 time pieces, the 2nd pin will be available at random from the Badge Seller for 200 pons.
Due to the high number of pons you can get in Mafia Town, you can quickly buy badges/pins from the 2 Badge Seller locations in acts like The Golden Vault, although if you already have enough pons you can just use quick locations like at the beginning of Train Rush, Contractual Obligations or the central area of Alpine Skyline.
Note: Do not buy the 1st pin when you have the "Skip Skippable Cutscenes" option turned on in the game settings. This will stop the 1st pin's effect from triggering and permanently lock you out of buying the 2nd pin needed for this achievement. The only solution after being locked out by this is to start a new save, collect another 15 time pieces and buy the two pins again.
Edit: This bug was reportedly fixed with the DLC update, however I'd recommend keeping the "Skip Skippable Cutscenes" option off just in case.