From Longman Dictionary of Contemporary Englishdance/sing/cook etc up a stormdance/sing/cook etc up a stormENERGETICto do something with all your energy They were dancing up a storm. → storm
Examples from the Corpus
dance/sing/cook etc up a storm• She danced up a storm at an Alexandria, Va., club where the Desperadoes played right after the election.• They are blowing trumpets singing up a storm and waving as they walk past us. 