Disarming a mobster is easy. Use the tommy gun, hold LT and use the right stick to aim for their right shoulder after they pull out their own gun (all the mobsters in the game seem to be right handed). A quick burst to that shoulder will always give you a disarm.
Simply run around Little Italy disarming all the mobsters you can find outside/inside the businesses. If you die, all the mobsters will respawn so you can go back to places you've already cleared out.
Once you have 10+, you'll need to wait out the remaining time to get the achievement. So just put your controller down and find something to do