to finish no matter what obstacles or cost
1867 Smyth Sailor’s Word-bk. pg. 103 A ship is ‘brought up to a bitter’ when the cable is allowed to run out to that stop. When a chain or rope is paid out to the bitter-end, no more remains to be let go…”
The end of the anchor line secured to a sturdy post on the deck called a bitt. The line was paid out in order to set the anchor. However, if the water was deeper than anticipated the rope would pay out to the bitter end . . . ooops.
The “bitter end” of any line is the loose, unsecured end.
“Meanwhile the bosun and his mates, together with the most experienced forecastle hands and tierers, roused out the best cable the Diane possessed, the most nearly new and unfrayed, a seventeen-inch cable that they turned end for end – no small undertaking in that confined space, since it weighed three and a half tons – and bent it to the best bower anchor by the wholly unworn end that had always been abaft the bitts: the bitter end. There was thought to be good luck attached to the bitter end, as well as greater strength.”
[Patrick O'Brian, The Thirteen Gun Salute, p. 299]