It turns out his ‘cousin’ is actually some weed he wants to get hold of. When the dealer won’t sell it to him, Big Smoke takes out one of them and leaves you to chase the other on foot across town as he’s too unfit to keep up.
It’s easiest to have an Uzi or other powerful weapon that you can sprint with as you’ll need to keep up with him and take him out. And remember it’s double tap on the run icon to jump a fence
A good tip is to watch the map to see which alleyway he is running down and take the main road. This will allow you to move faster than him as he will get slowed down climbing the various fences. Then you can intercept him when he emerges back onto the road.
If you’re a little slow catching him then he’ll jump into a car and you’ll need to pursue him on wheels. Jack a car in the usual way and either ram his vehicle or do a drive-by to blow up his car.
Take him out and you’ll have earned extra respect points.