Kind of like a "might as well go for it" kind of thing, in my language there are idioms that roughly translate to "you must finish everything on your plate, even if it's poison" or "you must follow the javelin you have hurled".
in for a penny, in for a pound
—used to say that a person should finish what he or she has started to do even though it may be difficult or expensive
“If you want to quit, I'll understand.” “No, I'm sure we can do this. In for a penny, in for a pound.”
- When someone complains that they are in a bad situation as a result of a decision they have made, or 2. when someone points out that the situation the other person is in is of their own making:
You have made your bed and now you must lie in it.
Bite the bullet
If someone bites the bullet, they accept that they have to do something unpleasant but necessary.
Tour operators may be forced to bite the bullet and cut prices.
Burn your boats
or Burn your bridges
To do something which forces you to continue with a particular course of action, and makes it impossible for you to return to an earlier situation
I didn't sell it because I didn't know how long I would be here. I didn't want to burn all my bridges.
"Face the music"
be confronted with the unpleasant consequences of one's actions.
This next one isn't exactly related to what you are asking for but still may be relevant to your context.
"Cross the Rubicon"
If you say that someone has crossed the Rubicon, you mean that they have reached a point where they cannot change a decision or course of action.
In keeping with the battle mindset you give, you could say you're willing to die on this hill. Also seen as a mountain I'm willing to die on.
It's a fight or an issue where for better or worse, you decide to draw a line in the sand or take a stand.
hill to die on (plural hills to die on)
(idiomatic) An issue to pursue with wholehearted conviction and/or single-minded focus, with little or no regard to the cost.
More in depth origins can be found in this question.
I think it's close to "play the hand you are dealt"
To use the resources which one actually has available; to operate realistically, within the limits of one's circumstances
Specifically for committing to one of two bad alternatives, I'd say "Pick your poison". When maintaining a bad status quo instead of taking a chance on a bad action, "Better the devil you know than the devil you don't." But for pushing through on a decision already made, I like the previous answer "In for a penny, in for a pound."
(a person's) "hands are tied"
Does not refer to a literal tying of hands. Merely that one person is unable to assist another due to some external pressure or situation.
e.g. "I'd love to help you out, but my hands are tied". or
"I wish I didn't have to let you go (fire you), but my hands are tied. Someone has to pay for the data leak."
"Don't switch/change/swap horses in mid-stream" is an idiom often used to say that the current course of action (and in particular the current leader) has been chosen and there is no option but to keep "crossing the stream" until the other side has been reached. It is attributed to Abraham Lincoln (source)
"Come hell or high water" immediately came to mind for me.
If one has to put a brave face on a sorry business you may say "He cracks hardy".
When it's a matter of pretending that everything is fine when things are actually going quite badly, "one puts up a good/a brave front".
If one managed to gain an advantage from something that he has to do and cannot avoid / accepted responsibility for or did cheerfuly and with interest smth. that he cannot avoid, you may say: "He made a virtue of necessity / made the best of a bad bargain".
Macbeth Act 2, Scene 2:
Things bad begun make themselves strong by ill.
could actually be used as an idiom though you might raise a few eyebrows. If you want to go for an applause you might try these lines from Act 3, Scene 4:
I am in blood Stepped in so far that, should I wade no more, Returning were as tedious as go o'er.
I think the answer is Shit or Bust.
According to Wiktionary it is Australian slang meaning: With extreme vigour and enthusiasm, where quality may be considered. However, efforts involve high risk, and therefore the potential for adverse outcomes. Vision exceeds regard for due care and consideration.
But according to Urban Dictionary it is a rephrasing of Royal Corps of Signals motto Certa Cito meaning "Swift and Sure". But don't ask me how you get from one to the other.
But it does seem to imply commitment to a course of action even if it is the wrong one.
"You need to pull the trigger on [doing something]" or just "it's time to pull the trigger."
This is definitely more American in context, but this indicates a choice must be made, and that choice cannot be undone, just as one cannot call a bullet back once it has been fired from a gun. The bullet is going to go where it's going to go, for better or for worse, and you're either going to hit your target, miss your target, or hit something you do not want to hit. But the phrase means that the person addressed needs to truly commit to something, even if they are not sure or are worried about the outcome, and then it is decided. It can be something completely trivial (getting a haircut, buying a new phone) or something serious (getting married, choosing a college to attend, buying a house, admitting a serious problem to someone, getting a serious problem fixed, etc).
Nail your colours to the mast, perhaps. The general idea being "...to defiantly display one's opinions and beliefs and also to show one's intention to hold on to those beliefs until the end".