Do a burnout (hold LT+RT) 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.