There are two cucial aspects you need to get right:
1. Really understanding, what each dimension means and why McKinsey scrutinizes it
2. Properly structuring the story to ensure that you address what McKinsey is really testing for
On point number 1, you need a former McKinsey interviewer to explain this to you. Not a consultant! An actual interviewer! Unfortunately the dimensions are almost impossible to properly explain if you have not been trained by the firm on what you need to test for. They are not self-explanatory (for example, "Leadership" has nothing to do with formally telling other people what to do or not to do; Personal Impact" has nothing to do with impact, and "Entrepreneurial Drive" has nothing to do with founding a company/organization).
On point number 2, the STAR framework is oftentimes mentioned. But I would definitely NOT recommend it, because it leaves out the most important aspect that McKinsey is looking for: the analysis and identification of the root causes of the existing problem. The STAR framework directly jumps from "Task" to "Action", wich is extremely problematioc. You need to explain the problem/challenge, why it was relevant, how you found out the root causes of the issue/challenge, and how you then addressed these root causes. A very natural part of this is also to describe such things like early failures in addressing the issue, which then helped you to understand the REAL reasons for the existing issue. It is very important that you concretely explain how you reached your understanding of these reasons and how you then consciously adapted your approach.