1
general::
Phrase(s): come hell or high water
Fig. no matter what happens. (Use hell with caution.) • I’ll be there tomorrow, come hell or high water. • Come hell or high water, I intend to own my own home.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Also, in spite of hell or high water. No matter what difficulty or obstacle, as in I'm going to finish this week, come hell or high water. This colloquial expression, alluding to the destructive forces of hellfire or flood, was first recorded in 1915 but is thought to be older., see HELL OR HIGH WATER.
American Heritage Idioms