To/Until the bitter end
To/Until the bitter end (English) — To follow something/someone through their actions or processes until their completion (often with known or perceived thoughts of failure, consequences). "We kept fighting short of ammo and food until the bitter end."
The bitter end of a line (a rope) is the very end where it has been seized (to prevent fraying, wear). Older natural fibers were much more susceptible to this. They had to be seized and dipped (tar of pitch). Those who touched them, tasted them. Those who had only two hands and needed three used their teeth and taste. Some say it has to do with bits (where ropes secure or are fed through) but old sailing ship sailors have different opinions.