give something your best shot
US /ɡɪv ˈsʌmθɪŋ jʊər bɛst ʃɑt/
UK /ɡɪv ˈsʌmθɪŋ jʊər bɛst ʃɑt/

1.
全力を尽くす, 最善を尽くす
to try as hard as you can to do something, even if you are not sure you will succeed
:
•
I don't know if I'll win, but I'm going to give it my best shot.
勝てるかわからないけど、全力を尽くすつもりだ。
•
Even if it's a tough challenge, you should always give it your best shot.
たとえ困難な挑戦であっても、常に全力を尽くすべきだ。