You'll have to get TM71 at the Battle Frontier for 80 BP or get a Pokemon that can learn it by leveling up. An easy way to get BP is to keep challenging and winning at a battle station and eventually the Frontier Brain will show up. Defeating them will give you 20 BP.
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an evelution stone
No
VulpixGrowlitheEevee
moon stone
You have to have the Engnima stone.