From Longman Dictionary of Contemporary EnglishAchilles' heelA·chil·les' heel /əˌkɪliːz ˈhiːl/ noun [countable] FAULT/something WRONGa weak part of someone’s character, which could cause them to fail at something I think Frank’s vanity is his Achilles' heel.
Examples from the Corpus
Achilles' heel• The team's offense is their Achilles' heel.• But, as at Loch Lomond, it was the hotel that was to prove the development's Achilles' heel.• Cara had one very big Achilles' heel - Barnaby Stewart.• Decoys that can confuse the homing sensor in the interceptor are the Achilles' heel of this system.• If not correctly understood it can be the Achilles' heel of a complicated chain of investigations.• It was her Achilles' heel.• Marketing traditionally has been an Achilles' heel for phone companies because of their monopoly mind-set.Origin Achilles' heel (1800-1900) From the story that the ancient Greek hero Achilles was dipped as a baby into the river Styx to protect him, but the part of his heel he was held by did not get wet, and so remained unprotected 