cheeky：Ex: You're getting far too cheeky! Ex: You did that on purpose, you cheeky little devil! Ex: Now don't be cheeky to your elders, young woman.
gall: Ex: the bank had the gall to demand a fee.
chutzpah: Ex: “has the chutzpah to claim a lock on God and morality” – New York Times Ex: It took a lot of chutzpah to talk to your boss like that.
nerve: Ex: You have a lot of nerve. Ex: You've got some nerve! Ex: she's got a nerve wearing that short skirt with those legs.
have the neck to do sth.: Probably BrE No written evidence is provided in the New Oxford English Dictionary
hide: Ex: 'I'm sorry I called you a pig.' 'My hide's thick enough; it didn't bother me.'
bold-faced: Ex: a bold-faced lie. Ex: He had the bold-faced effrontery to ask for a raise.