break your back
break (one's) back
To put forth a great deal of effort. I've been breaking my back trying to get a passing grade this semester, so failing by two measly points is incredibly frustrating. Don't break your back trying to please these people—they'll never appreciate it.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
break your back
If you break your back to do something, you work extremely hard to try to do it. When you're breaking your back to make a business work, it's going to cut into your time with family. `I had been travelling all over the country, breaking my back just to get a job,' she says.
Collins COBUILD Idioms Dictionary, 3rd ed. © HarperCollins Publishers 2012
break your ˈback doing something/to do something
work very hard to achieve something: I’ve been breaking my back to sell as many books as I can. ▶ ˈback-breaking adj. (of physical work) very hard and tiringFarlex Partner Idioms Dictionary © Farlex 2017