Make sure your party is around level 48-50. This Shadow has no weaknesses, so just pummel it with your strongest attacks. Teddie is great for this battle, as he's fairly resilient and should have Mediarama and Matarukaja. Buffing isn't a must, but will definitely help speed the battle up; if using your own Persona to buff your party, use one with a high Strength stat so you can rely on physical attacks that don't use up valuable SP. Dominating Machine will always use Power Charge before using Herculean Strike, so you'll have a free move available to heal/buff. When its HP is low, it will Stand By until it can use Last Resort (usually when its HP is down to a sliver).
