Achilles heel :
A person's only vulnerable spot; a serious or fatal weakness. In Greek mythology, the nymph Thetis dipped her infant son Achilles in the water of the River Styx to make him immortal, but the heel by which she held him was not touched by the water; he was ultimately killed in battle by an arrow wound in this one vulnerable spot. 1998 Times The inclination to outlaw that of which it disapproves... is, if not the cloven hoof beneath the hem of Tony Blair's Government, certainly its Achilles heel.