Personally, I've beaten Reborn a few times without EV Training or IV Breeding. So no, I would not say it's a requirement. The only thing I do is sometimes try to get is a pokemon with a decent nature. You have to remember, as battles become more difficult, you will also have access to better items for your pokemon to hold and better healing items to use in battle (revives, ultra potions, etc.), and unless you're against using them, you'll have less of a hard time.