So, for some reason you want to go in blasting and come out before they know what's hit em, right? It's harder than it may seem, as often you'll find yourself up against a dozen craft rather than the small convoy you just attacked ...
Hit and Run
In these situations, its best to know what your escape routes are. For instance, you could be looking for a lane and in the meantime more ships are chasing you and lining up their targeting scanners. So, find out some good escape routes, nearby lanes, nearby debris fields or just empty space (more on that later).
Once you've got the authorities mad, they'll stay mad at you until you dock at a station. Remember, you won't be allowed to dock at a hostile planet or station, but you will be allowed to dock with hostile trade lanes and jumpgates.. so remember that. Once you've docked somewhere, you can get back in your ship and return to the scene of the crime to find they've forgotten about your little outburst, but only as long as your reputation with them is either Neutral or Friendly.
By far the easiest way to get someone to hate you is to attack their storage depots. The more canisters you blow up on each depot, the less popular you'll get with the faction who owns it. Once a depot becomes hostile to you (it turns red), you should do as much damage as you can and get out of there FAST, because nothing gets cops out like a depot attack, and you might be facing up to twelve or more police vehicles, including any allies if they happen to be close.
Be warned, if you only want to make a faction Neutral, don't blow up a whole bunch of their depot containers, otherwise you might find that they become Hostile because you blew up too much of their stuff. Make sure you check your reputation regularly to learn what effects your actions have on your notoriety.
Don't forget to use Drift to make good your escape, especially if the locals carry Cruise Disruptors. Besides its safer to drift away a couple of clicks before engaging cruise engines, especially as you can't do anything but maneuver during the cruise countdown.
Tractor in anything valuable, don't blow up a supply depot or a couple ships and then run off without grabbing the loot because you panicked! Notice you can't tractor while cruising ... but you can while Drifting!