The phrase "aim of shooting" is correct and usable in written English.
It can be used in contexts related to sports, photography, or any activity involving aiming and shooting at a target.
Example: "The aim of shooting in archery is to hit the bullseye consistently."
Alternatives: "goal of shooting" or "objective of shooting".
I'm planning to fund-raise at the end of this year, with the aim of shooting the rest of it next year.
The Forestry Commission has said its annual cull would begin later this month with the aim of shooting 100 animals by January.
For the North Koreans, the aim of shooting a ballistic missile targeting the Andersen Air Force Base is to demonstrate that they have the capacity to damage or destroy one key pillar of U.S. nuclear forces in Asia.
The Bush administration says that the defense system will be capable of shooting down missiles aimed at the United States or its NATO allies, and that it is necessary to fend off threats from nations like Iran and North Korea.
President Obama has joined in, accusing Mr Romney of shooting first and aiming later saying: "As president, one of the things I've learned is you can't do that, that it's important for you to make sure that the statements you make are backed up by the facts, and that you've thought through the ramifications before you make them".
While some people look to the stars to make a wish, the ladies of SGAC aim to shoot for the moon and beyond.
Aim to shoot within 30 minutes of sunset to stop the orange glow from street lamps from washing out sky colours.
I was, for very good reason, taken to task on the feedback page by one of the students in this class for presenting playfully in lecture, in the context of our discussion of punishment, an example of somebody who aimed to shoot somebody and failed or succeeded at his aim on a day after there had been a shooting in New Haven.
Generally, it's best to orient your body in order to see the line of your aim while shooting comfortably; you may not move or leave your chair.
