Missions that allow you to rack up cars quickly are the prison escape, rescuing Jacks, reaching Tobias, and any other mission where you are being actively chased by cops/enemies. I got my achievement during the Rescuing Jacks mission. Both the Jacks and Tobias missions are convoy-type missions. So if for some reason you don't have this achievement after Tobias, you can always use Convoy side missions to get the last few.
Skills to have should be Hacking skills like Barricades, Spikes, Blockers, Traffic Lights, and most importantly Steam Pipes. While most of the previous ones requires a little timing, exploding the Steam Pipes under the roads will cause a massive explosion that can take out 2 cars possibly even 3 if you're lucky. This requires you to meet Clara in Act 1 to unlock the rest of your skills. You'll need to do some Crimes and Gang Hideouts to get the necessary Skill Points to buy this skill. The rest are either default or skills you purchase before Steam Pipes.
That's the prep, here's the how. You will actually get a prompt as to the best time to trigger these hacks. The icon for the hack will start to 'count down' so to speak until it starts flashing blue and says "Neutralize" when enemy vehicles get close to these triggers. This is when you want to hit these triggers as they are then guaranteed to take out at least one car. You can use Focus if you want to slow time and better allow you to trigger the event at the best time.
Lastly, you don't have to actively seek out and do this achievement. It will come as you do the story missions easily. You'll probably take out dozens of vehicles before the end of this game.