Achilles heel
Concise Oxford English Dictionary © 2008 Oxford University Press:
Achilles heel /əˈkɪliːz/
▶noun a weakness or vulnerable point.
– origin C19: alluding to the mythological Greek hero Achilles, whose mother plunged him into the River Styx when he was a baby, thus making his body invulnerable except for the heel by which she held him.
'Achilles heel' also found in these Oxford entries:

