not to leave a stone unturned

"not to leave a stone unturned" — means that the person is going to look everywhere, turn over every rock. The meaning has broadened to mean: I will do everything in my power — сделать всё, что в силах.

see also

[lay oneself out to do sth]
[fall over backwards to do sth]
[go out of one's way to do sth]
[pull out all the stops]
[go an extra mile]
[изо всех сил]