Dic: Have a shot at; Have a go at; Have a crack at

1. have a shot at something : also, take a shot at something

to try to do something, often for the first time.

• He's proven himself to be a talented actor and now he's having a shot at directing his first play.
  

... Cambridge International Dictionary of Idioms,
http://idioms.thefreedictionary.com/shot

2. have a crack at: also,

• get(or have) a go at something;
• get(or have) a shot at something;
• get(or have) a whack at something;
• take a crack at.
  

Make an attempt or have a turn at doing something. For example:

• Let me have a crack at assembling it, or
• I had a shot at it but failed, or
• Dad thinks he can--let him have a go at it, or
• Dave had a whack at changing the tire, or
• Jane wants to take a crack at it.

The oldest of these colloquialisms is have a shot at, alluding to firing a gun and first recorded in 1756; crack and go date from the 1830s, and whack from the late 1800s.

... The American Heritage Dictionary of Idioms,
http://www.answers.com/topic/have-a-crack-at

Cf: have a shot at someone (Australian, informal): to criticize someone.

• It's clear the film's director was having a shot at the government.