This achievement requires you to achieve a speed of 240 mph with a vehicle in the game.
To do this, you can upgrade any of the high end cars with cards from the tuning shop to get your car as close to 399 as possible while also getting your top speed over 240, or you can just purchase the Koenigsegg Regera and not have to upgrade it. The downside to this is that it costs 880k credits. Now you need to purchase the Regera anyways for another achievement, but you can actually get this achievement way before you even have the Regera unlocked, and it won't cost you a dime, contrary to the other guide here which states you need to wait until basically the end of the game to even have a shot at unlocking this.
Very early on in the story, you will have a mission that tasks you with stealing a high tech Regera out of a moving truck (Mission is called The Highway Heist). After you complete this for the first time, it will be on the map and you can replay it again. Play the mission normally until you steal the Regera and have to drive it to the airport. There will be a very long straight section you'll be driving on as you get closer to the air field and the checkpoint will tell you to make a sharp right turn towards the air field. I noticed I was approaching 240 mph as I approached this checkpoint, so instead of braking and turning right I kept going, as the highway continues on straight, and hit 240 shortly after.
The key for this is to make sure you save up your nitrous and ensure you do your best not to hit anything as it will hurt your speed pretty bad. I crashed in the tunnel as soon as the cops were called however and still managed to gather up enough speed to get the achievement.
Be careful though as you are timed and once you run out of time you'll fail the mission. I'm not too sure if you have to restart the whole mission or not if you fail, but keep trying if you don't succeed right away as this is the fastest and cheapest way to get this achievement.