General:
* Making a mark
* Making a difference
* Leaving a legacy
* Finding his purpose
* Achieving his goals
* Living a fulfilling life
* Making the most of his life
* Having a meaningful existence
More specific:
* Succeeding in his career
* Building a family
* Making a contribution to society
* Making a name for himself
* Living life to the fullest
* Following his passion
* Finding happiness
* Experiencing life fully
The best synonym for "doing something with his life" will depend on the context and what you want to emphasize.