1
general::
Conceited, haughty, as in She was too high and mighty to make her own bed. This expression originally alluded to high-born rulers and was being transferred to the merely arrogant by the mid-1600s.
American Heritage Idioms
2
general::
Phrase(s): high-and-mighty
Fig. self-important and arrogant. • I don’t know why William is so high-and-mighty. He’s no better than the rest of us. • The boss acts high-and-mighty because he can fire us all.
McGrawhill's American Idioms And Phrasal Verbs