Legendary and Mythical Pokémon.
How to unlock the legendary and mythical Pokémon from the main game. Three are story-locked (you can't miss them), six need crafted summoning items, and Mew is the reward for the endgame Slate hunt. The free 2.0.0 update also added the Mythical Pokémon Manaphy, who teaches Ditto the move Dive.
Articuno
One of the three Legendary Birds. Befriend all three to unlock the Tidal Bell recipe for Lugia.
Zapdos
Second Legendary Bird for the Tidal Bell / Lugia chain.
Moltres
Third Legendary Bird. Befriending all three grants the Tidal Bell recipe.
Mewtwo
The Sparkling Skylands meeting only logs it in the dex; the actual befriend happens on its Dream Island.
Mew
The true endgame goal. The Slate hunt spans all four regions.
Raikou
One of the three Legendary Beasts. Befriend all three to unlock the Clear Bell recipe for Ho-Oh.
Entei
Second Legendary Beast for the Clear Bell / Ho-Oh chain.
Suicune
Third Legendary Beast. Befriending all three grants the Clear Bell recipe.
Lugia
Silver Feathers drop from Lugia as it passes overhead; gather them to craft the bell.
Ho-Oh
Rainbow Feathers drop as Ho-Oh passes overhead; gather them to craft the bell.
Kyogre
You can't miss it. It drives the rainstorm that revives the wasteland; afterward it re-appears at random from the ocean.
Volcanion
Mythical tied to the volcanic region's plot.