To get this play style, you need to kill people by executing them with a silenced pistol. The kills must be stealth kills. Walk up behind them with your Silver Ballers equipped and hit the X/Square button to execute this. Do it several times without being seen.
I found Countdown to be the easiest map. There are plenty of guards to kill and if you play it smart, you can cut through them pretty quickly. You could do it on any level as long as you have a silenced weapon (doesn't have to be Silver Ballers) so if you have a favorite, just use that level instead.
