Bat an eye/eyelid
Usually occurs in the negative as in did not bat an eye/eyelid, which means to show indifference or lack of reaction. Bat is an old word from the 1400s, originally a falconry term. When hunting, birds bat their wings, it means they beat or flutter their wings. To bat an eye or eyelid means to blink and dates from the late 16th/early 17th century but it was not until the 19th century that its negative form came to denote indifference or lack of reaction.