give something your best shot
give (something) (one's) best shot
To put one's utmost energy, effort, or determination into doing something. I gave writing my best shot, but I just don't think I can make a career out of it. Don't worry about being new, just give it your best shot.
give something your best shotINFORMAL
COMMON If you give something difficult your best shot, you try as hard as you can to achieve it. I don't think the Republic have enough quality players to become World Champions, but they'll give it their best shot. As long as I play tennis, I'll keep coming back and giving Wimbledon my best shot. Note: You can also simply describe a course of action as someone's best shot when it is the best chance they have of achieving something. Analysts say Canada's best shot at economic recovery is continued growth in the United States.