Pal Metal Chestplate

The Traveling Merchant will not offer this until you are holding one of the crossover pets when you speak to him. Any of Digtoise, Cattiva, Foxparks or either Chillet does the job, and the check looks at your Piggy Bank as well as your inventory, so one parked in portable storage still counts. Talk to him empty handed and the two pieces are simply absent from the list, which is why the set looks unobtainable until somebody tells you the trick.

Two parts only, a chestplate and leggings, both cosmetic and both headed for the social slots. There is no helmet, so the head stays free for whatever else you want on top of it.

Those versions shipped the items before there was any route to them, so an older build can have the set sitting in its files while the merchant never once stocks it. A later patch turned the shop condition on and brought them level with the desktop version.