Target creature you control gets +X/+X until end of turn. Then it fights up to one target creature you don't control.
If the creature you control is an illegal target as Primal Might tries to resolve, no creature gets +X/+X. If that creature is a legal target but the creature you don't control isn't, it still gets +X/+X.
If you choose two target creatures and either target is an illegal target as Primal Might tries to resolve, neither creature will deal or be dealt damage.
You can cast Primal Might targeting only the creature you control.
You can cast Primal Might with 0 as the value of X to just have the two target creatures fight.