break one's neck/back to do sth：尽最大努力；尽一切可能

e.g. I broke my neck to get here on time.

我紧赶慢赶总算准时到了这里。

That's the last time I'll break my neck to help you.

这是我最后一次舍命助君一臂之力。

e.g. There is no point in breaking your back. Take your time.

你没有必要这样卖命，慢慢来，不要着急。