Do a burnout (hold +) until one tire pops before starting a pursuit. Waiting for a spike strip in the middle of a pursuit is making it harder on yourself.
Find a cop, indicated by blue arrows on your mini-map. Get a takedown on the cop so the pursuit starts and the cop is disabled right away. I chose to use the Raptor for this purpose as it's size & weight almost guarantees a takedown.
Drive away as fast as you can before the other cops get close enough to see you. The achievement will unlock after you've escaped and left cooldown mode.
Another way of doing this is do the burnout beforehand on the motorway and drive as fast as possible with the intention of taking out a police car with the first hit. This way you can just drive off while they are crashed.