What is a strong expression for someone going though a hard ordeal to achieve something important? For example a mother who has lost her children will _______ to get them back.
Here are three fitting idioms for "going through a hard ordeal to achieve something important":
1) move heaven and earth idiom: Exert the utmost effort, as in I'd move heaven and earth to get an apartment here. This hyperbolic expression was first recorded in 1792.
2) fight tooth and nail idiom: Engage in vigorous combat or make a strenuous effort, using all one's resources. For example, I'm going to fight tooth and nail for that promotion. This expression, with its allusion to biting and scratching, was first recorded in 1576.
3) go through hell idiom: to have a very unpleasant experience, especially one that lasts for a long period of time. The poor woman's been going through hell over the last few months, not knowing whether her son was alive or dead.
(All linked definitions from The Free Dictionary)
One that comes to mind that fits right into your sentences is to move mountains (Farlex Free Dictionary).
- if someone or someone's beliefs or feelings can move mountains, they can achieve something that is very difficult. If faith can move mountains, we'll win the Cup.
- if you would move mountains for someone, they are so important to you that you would do anything to please them. He'd move mountains for her but she treats him like dirt.
She will be disposed to go through hell and high water to get them back:
Fig. through all sorts of severe difficulties. (Use hell with caution.)
- You'll have to go through hell and high water to accomplish your goal, but it'll be worth it.
The Free Dictionary
You're asking for an expression describing an extreme sacrifice in exchange for great reward. One common such expression is to sell your soul, suggesting you are willing to give up your own freedom and life for your goal. This often has negative connotations and is frequently related to material gains, but could just as easily describe the desparation a mother feels searching for her lost child. In fact, many folk tales and fantasies depict a character quite literally exchanging their soul or the essence of their being with a godlike figure for some power, wealth, or the return of a lost loved one.
Another expression is the willingness to go to the ends of the earth searching for your goal. This alludes to the archaic belief that the world has edge-like boundaries far beyond the realm of experience most people can claim to know. Being willing to travel to the ends of the earth, therefore, implies being willing to leave your life and the whole known world behind, likely spending the rest of your days in search of your goal.
If the important thing to be achieved is spending time with someone with whom you're infatuated, then you might say that you would crawl on your hands and knees over broken glass just to do X for/with that person:
do anything to be closer to her, worship the ground she walks on I'm so in love I'd crawl on my hands and knees over miles of broken glass to see her photo.
-- From the Babylon online dictionary
Choosing X to be some utterly trifling and/or depraved activity can enhance the comic effect.
Stop at nothing is a pretty solid option.
Do everything in one's power, be prevented by no obstacle, as in She'll stop at nothing to get her revenge. This expression was first recorded in John Dryden's Aurengzebe (1676): "The World is made for the bold impious man; Who stops at nothing, seizes all he can."
The popularity of the movie The Shawshank Redemption has caused a line to enter the common vernacular: "...who crawled through a river of shit, and came out clean on the other side."
Reading your question, that line was the first thing to come to my mind.
It can be modified to fit grammatically into different sentences and still maintain its meaning.
The woman who ultimately saved her children crawled through a river of shit, but the story has a happy ending.
Spoiler alert: from The Shawshank Redemption
Running the gauntlet, you could say.