Instructions
Complete chapter 20 to finish the game's main story and watch the ending credits. Afterwards, you will receive a message that you can graduate from the guild by taking an exam.
Make your way through all thirteen floors of the Mystifying Forest after you are sent there. When you reach the clearing at the end, you will fall into a trap.
Win the battle to be automatically taken to Luminous Spring, which is where Pokémon evolve in this game. The sunlight shining on the spring indicates that you can use it from now on.
Select "Evolve" when at the spring and then select the Pokémon that you want to evolve. It does not have to be in your party to evolve. The text at the bottom of the status screen of each Pokémon indicates whether it is able to evolve yet. Your two starter Pokémon are the only two that are not able to evolve at this point, but you can rectify this by completing a few more missions.
Keep completing missions until you are given the chance to battle the final boss, Darkrai. Defeat it and a Pokémon named Manaphy will join your team. This will unlock the Marine Resort.
Recruit Palkia, which is found at the Spacial Rift. Return to Luminous Springs. Select "Evolve" and you will find that your starting Pokémon are now able to evolve as well.