This is accomplished at the end of Chapter 11. When you are sent to settle the score with the Irish after your house is burned down. After you clear out the bar (you should rob the register), head out back and your target will be getting into his car. You can either chase him in your car and run him down, or get a lucky shot at him as his car pulls out of the alley.
**You can miss this achievement and have the story continue. I missed it the first time, and had to reload chapter 11 from the beginning and play through the whole chapter to get this chance again, so it is worth trying to get as you play through the first time.