like hell

1.  Recklessly, extremely, as in We ran like hell to catch the train. [Mid-1800s]
2.  Not at all, on the contrary, as in You think I'll call her stupid? Like hell I will! or Like hell I can't say that to Bob. [Late 1800s]

The adverb has 2 meanings:

Meaning #1: (informal) with great speed or effort or intensity
  Synonyms: like mad, like crazy, like sin, like thunder, like the devil

Meaning #2: used ironically to indicate the opposite of what is stated