In ranked multiplayer matches, you gain 1 nitro for each 20x multiplier you earn. So you're gonna need to get at least 200x multiplier to unlock the achievement.
Getting this kind of multiplier in a ranked match will probably require doing it with a friend or being lucky enough not to get your string stolen. Also, remember that, at the end of the last lap, if you don't have the required total, you don't have to cross the finish line (you'll only lose the bonus for finishing the race). You can keep on "near missing" stuff until you get it.
Also, you have 5 slots for your nitro. If all your slots are full, you're not earning new nitro. In order to gain 10, you're gonna need to spend some regularly. It can be quite tricky because if you're not planning right, using a nitro at the wrong moment can make you break your string...
Overall, I found that Overdrive 1 in Backlot Battle was the easiest to get the achievement. After 3 laps, you typically have around 180x multiplier and the last straight to the finish line is composed of 2 corridors. So you can easily drive around it to get your multiplier over 200x.