Guys. Its a Kalos-bred Umbreon. Heal Bell is Gen 4 exclusive, Foul Play is Gen 5 tutor exclusive. The only Dark moves available to it are Payback, Bite, Dark Pulse, HP Dark, and Snarl.
Its Calm, so we can disregard the first two. HP Dark is.. no. Umbreon is slow, so flinching with Dark Pulse isn't doing much. Snarl completely fucks over every special attacker in the game that doesn't have Competitive, and White Smoke Torkoal (lol). Against physical / mixed foes, Dark Pulse and Snarl are both hitting for just barely enough damage to negate Leftovers anyway. The stat drops also encourage switching to rack residual damage in Singles, I imagine (I haven't done Singles since early Gen 5, so I don't feel confident giving advice there).
In doubles, Snarl hits both foes, and in most cases this is beneficial (breaking Sash/Sturdy, crippling Special attackers), even though there are bad cases like Justified, Contrary, and Defiant.
In short, Snarl makes Umbreon stupidly bulky on the special side, while Dark Pulse really does nothing as a base 60 Sp. Atk is going nowhere. I realize no one uses Snarl, but I've personally had a lot of success with it. In Doubles, Snarl is twice as dickish. :P
Similar to how a lot of things run Icy Wind over the much stronger Ice Beam: support over damage.
Other moves, you have a decent pick with Helping Hand, Taunt, Charm, Baby-Doll Eyes, Screech, and Toxic for doubles, singles, scratch off everything except Taunt. EVs, you could get creative with Speed or something but a standard max HP/Sp. Def spread would probably work just fine. I actually use a Calm Umbreon in Doubles now and again with Snarl / Wish / Protect / Helping Hand, with 252 HP, 4 Def, 252 Sp. Def and it's been fine.
I hope some of that is useful. I'm not aiming to argue, its simply opinion and some experience.