This idiom or expression has to do with:

Having an injection, as in:
A. Have you got your shot yet?
B. I’m not going to. I don’t believe in getting flu shots!!

Used with "at," having a chance or an opportunity, as in:
A. Why are you directing such a small budget movie?
B. This is my first shot at directing any kind of movie, and I’m not gonna miss it!!

This idiom or expression means:

Some chance.
An opportunity.

Give him half a chance. Take it easy on him.

This idiom or expression like phrase means:

A chance.
An opportunity.

They deserve the opportunity to prove themselves. Give them a fair shot.

This idiom or expression has to do with:

Finding an opportunity.
Using or creating an opportunity.

A. Are you having any luck getting your book published? I know have it ready
B. I don’t know anyone in the business. If I could only get my foot in the door!

This idiom or expression has to do with:

Being too late.
Missing an opportunity.

Hey, make a decision or you’re gonna miss the boat.

This idiom or expression represents:

More opportunities, usually used to sympathize with a girl or boy who's been hurt romantically.

Don’t worry, there are plenty of other fish in the sea. There will be other (romantic) opportunities.