Even if Pokémon Masters highlights the ‘Collection’ aspect with the different Trainer/Pokémon Duos, it is not possible to fill a Pokédex with creatures. That said, you will want to “catch” all the available Pairs and evolve certain Pokémon. Here’s how to do it.
How to evolve a Pokémon?
In Pokémon Masters, there are no evolution or level-up items to evolve your Pokémon. In reality, you do have to reach a level, but it is the level of your Duo (trainer and Pokémon). To increase this level, you can use Strengthening Manuals that you get in Bonus Areas or simply do battles.
Once the required level is reached for evolution, a mission is then unlocked and you will have to complete it. This will activate the evolution of the Pokémon.
Please note, to be able to participate in this special mission, you must have an evolution nugget (for stages 1) and an evolution aggregate (for stages 2). This can be obtained in the Game Shop in exchange for 1000 coins, or use the item exchange.