You’re determined to do what you say you will do, no matter what happens, no matter what difficulties or obstacles get in your way.
The phrase has alliteration, which makes it fun to say, and easy to apply to almost anything which is difficult to overcome. It originated in America and the earliest reference appears to be from the Iowa newspaper The Burlington Weekly Hawk Eye, in May 1882.
The earliest examples strongly suggest cattle ranching as the origin, particularly cattle drives to railheads in the Midwest during the latter part of the 1800s. Paul Wellman published a book in 1939 with the title, Trampling Herd: the Story of the Cattle Range in America. He writes: “‘In spite of hell and high water’ is a legacy of the cattle trail when the cowboys drove their horn-spiked masses of longhorns through high water at every river and continuous hell between.” The prairies in summer with heat, dust, and flies would certainly have qualified as ‘hell.’
In November 1905, The Washington Post published an article about an old-time cattleman. “He prospered in those palmy days until he became the largest cattle owner in the territory and felt able to take his regular blowout in St Louis, until 1884, when, between the alien land law, drought and rustlers, and the ‘hell and high water of the cattlemen,’ he … walked out of the Kansas City stock yards a few hundred thousand dollars worse off and no cattle worth putting an iron on, much less pulling grass by hand to feed.”
A similar phrase from the southern US is “Lord willing and the creek don’t rise,” meaning essentially “if all goes well; barring any disaster.”
Wikipedia says that some contracts contain a ‘hell or high water’ clause. Such contracts are usually leases, providing that the payments must continue irrespective of any difficulties which the paying party may encounter (usually in relation to the operation of the leased asset). The clause usually forms part of a parent company guarantee. It is intended to limit the applicability of the doctrines of impossibility or frustration of purpose.
All that sounds very ‘legal’ and not what I choose to deal with on a lazy Sunday morning. However, your mileage may vary.