have a shot at (someone or something)
1. To try something. A: "Do you want to try driving my car, to see how you like it?" B: "Yeah, sure, I'll have a shot at it."
2. To have a chance to achieve, attain, or have success in something. Do you really think I have a shot at winning this thing?
3. To criticize someone or something. Primarily heard in Australia. I had a shot at him this morning, so he already knows I'm unhappy with his proposal.