"One variety of the mysterious Mega Stones. Have Archilles hold it, and this stone will enable it to Mega Evolve."
Archillesite can be bought from the Bealbeach Department Store on Mondays for 50,000 or obtained for free if you have an Archilles in your party after defeating gym leader Vaeryn and you select that Archilles after being asked what Pokémon you would like to be able to Mega Evolve.