Target creature you control gets +1/+2 until end of turn. It fights target creature you don't control. (Each deals damage equal to its power to the other.)
If the creature you control is an illegal target as Epic Confrontation tries to resolve, the creature you control won't get +1/+2. If that creature is a legal target but the creature you don't control isn't, your creature will still get +1/+2. In both cases, neither creature will deal or be dealt damage.
You can't cast Epic Confrontation unless you choose both a creature you control and a creature you don't control as targets.