>>29564875The Pokemon can be any level. If you want to check the IVs yourself using a calculator, you can figure out EXACTLY what each IV is, and that does require your pokemon to be a higher level to be more accurate. But the IV checker will tell you if your pokemon's IVs are perfect, which is all you need to know, so there's no point in that.
Make sure you have a destiny knot and an everstone. Give ditto the everstone so its modest nature passes on to the children. Give your other parent the destiny knot so the child inherits 5 out of 6 IVs from the parents rather than 3. Then just pump out eggs until you get something better than what you have. You only need a 5iv eevee (in the right stats) for it to be battle ready, and yours currently has 4, so one step up will get you where you need to be. If you were starting with, say, a 2iv umbreon parent, you would replace it with the first 3iv you get, then 4iv, until your parents are the best they can be.
I don't think Umbreon has any mixed attacking applications, so if your current 4iv parent has both attack and special attack, it's essentially a 3iv parent, because one of those attack stats is useless to you.