Put a +1/+1 counter on target creature you control. Then that creature fights target creature you don't control. (Each deals damage equal to its power to the other.)
If either target is an illegal target as Hunt the Weak resolves, neither creature will deal or be dealt damage.
If the creature you control is an illegal target as Hunt the Weak tries to resolve, you won't put a +1/+1 counter on it. If that creature is a legal target but the other creature isn't, you'll still put the counter on the creature you control.
You can't cast Hunt the Weak unless you choose both a creature you control and a creature you don't control as targets.