It is recommended you combine this achievement with "Most Wanted". Before anything else, make sure you have no quest active or the achievement won't pop and make sure you are prepared. Get yourself some armor, a shield, a sword, and lots of bolts.
To make your wanted rating go higher, you need to kill the guard because killing civilians will take forever to get to the maximum wanted rating. For this part take your time and kill one enemy at a time. The Crossbow can be pretty useful to kill the guard at a distance.
The best way to survive in a five wanted level chase is to run around in big circle and make sure to pick up armor and food to regain health every now and then to stay alive.
A good spot for free food is in front of the Butcher's store in the first city, with some free armor two blocks to the West.