Task List/badge lv1
You know those sparkly stone things that comes out of the Eggs you hatch? Those are called Gems, and they come in as many types as there are Pokémon Types. If you hatch ten of a certain type of Gem, you can start construction on your first Gemwish Badge! Once you start construction you should consider getting Pokémon to evolve for the badge.
Pokémon that change its type as well as Delta Species (Pokémon with an abnormal typing) count for the construction as long as the type required is involved in the Evolution, whether it is before evolving or afterwards.
For more information on the Wishforge, check the Wiki.