Hyper Training is a feature introduced in Generation VII. It is a more powerful version of Super Training.
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In Pokémon Sun and Pokémon Moon, you can draw forth a Pokémon’s power to its utmost limit with Hyper Training.
Pokémon grow stronger by raising their levels and increasing their base stats. However, their power is still affected by the individual strengths innate to each Pokémon. Now, with Hyper Training, Pokémon that have grown to Lv. 100 will be able to increase their individual strengths, which has never been possible before.
With Hyper Training, you can increase the strength of the Lv. 100 Pokémon you've been adventuring with!
Hyper Training is done by Mr. Hyper—a man who loves to collect Bottle Caps. He can be found somewhere in the Alola region. If you bring him Bottle Caps, which you can obtain in Pokémon Sun and Pokémon Moon, you’ll be able to improve your Pokémon's stats with Hyper Training.
The Event Magearna you'll be able to get will be holding a Bottle Cap, a precious item needed for Hyper Training. With a Bottle Cap, you can perform Hyper Training on any Pokémon. Get Magearna on your team and try out Hyper Training for yourself!From Pokémon.com