My advice is to do this achievement after you finished the Main Story as you will have likely outfitted your ship with the best gear the game has to offer. Here are some things to keep in mind when going for this achievement.
- Equip repair bots and boosters. These things can be lifesavers at a moment notice. You never know when you might get overwhelmed and lose all your progress. So save whenever it's all calm and quiet.
- Your Criminal Record is tracked separately between Galactic Union, Rebels, and Neutral systems. Stick to destroying police patrols in just one kind of systems. This way you can retreat and repair your ship at a Trade Station on a non-hostile system. Otherwise you will have pay a ridiculous amount of CRs to use ("Hack") a Trade Station.
- Destroying police patrols isn't difficult until the military shows up. That happens when your Criminal Record reaches 5 stars. They send in one military cruiser that's difficult to take out even with the best weapons in the game on Easy Mode. So when you see one coming on your Target List, either take it head on or run for your life. The cruiser takes awhile for it to get within your range, so take this opportunity to run away. If not, equip your missile launcher and start firing until it blows up or you do. If possible try to get around to it's rear where your less likely to be fired upon. You will have to deal with a new military cruiser every 5 minutes the longer you stay in the system.
- Stay within 4u of the Warp Gate if you want no new police patrols to chase you. Remember you can't escape to another system if there are any enemies within 4u of you.
- Pro Tip: The bottom of any Trade Station is safe. If you want to escape anyone from shooting at you while your shields recharge just circle underneath the trade station. As you do so, have your turrets lock on and shoot down any passing enemies. If a military cruiser reaches a Trade Station this will be the easiest way to take it out.
- Pro Tip: To lower your Criminal Record head on over to a different Territory ie. Terran to Mortok, Thul to Raptor. Repeat this 3x and your 5 star wanted level should disappear. This proves easier to do once you obtain the Zero Point Drive which you receive after you collect all the artifacts.