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Eevium Z: After completing the Pokémon League, head to the mega mart beside the Battle Royale stadium, and at one of the checklanes, a man will tell you about a bunch of trainers with different Eevee forms. Beat them all, and go back to him and (I presume) he'll give you the Eevium Z.
Also according to the trainer in Diglet Cave near the entrance, apparently if you beat all the trainers that challenge with Z-Crystals, you can get the ultimate in Z crystals or something like that. I'm not sure what he gives though.