Spike strips start to be deployed at heat level 3. It will count as avoided if you either go past the spike strip or if you do a U-turn before you hit it. Be sure to avoid them at all costs because hitting one will almost certainly result in being busted. To unlock this achievement, you must dodge 5 of them and successfully evade the pursuit
Usually, spike strips and their location are announced over the police radio to 'warn' other officers(despite the fact that spike strips never actually harm police cars). Pay attention to these messages, they often help you prepare for upcoming spike strips.
Use your speedbreaker whenever you see a potential spike strip unit that you have not prepared for; it will provide you with a little extra time to navigate away. While the speedbreaker is in effect, your car will receive a hefty boost in handling, allowing you to make impossibly tight turns. The same applies to Rhino SUV units, which can and will ruin your attempt.
Hat tip to MeesterLuther
for additional information.