Slipstreaming happens when you closely follow the car in front of you (best done on straights). That way, you exploit the slipstream created by the car in front of you, as your car has much less drag and increased speed, enabling you to easier overtake your opponent.Imagine your car getting sucked closer to the rear of the car in front of you.
Slipstreaming for a total of 10 minutes will take a while, even if you try boosting it.
There are two ways of getting this achievement:
1. The average duration of slipstreaming to overtake a car is about 3-5 seconds - this multiplied by 23 (for the maximum of cars you can overtake without falling back and doing it again) comes to 92 seconds.
Building on this, you will have 1:30 minutes worth of slipstreaming for overtaking the whole field in a Grand Prix. Of course, this only applies if you count an average of 4 seconds for each time you slipstream. Realistically, I would say you'll get 50 seconds to one minute worth of slipstreaming for overtaking 23 cars.
Your best bet is to set up a series of 3-lap races (maybe even 10% races), set the A.I. difficulty to Amateur and make sure to fall back at the beginning of the Grand Prix in order to overtake all cars on the track as fast as possible by using slipstreaming before overtaking.
Also make sure to use a fast car - Red Bull, McLaren, Ferrari - that has KERS at its disposal.
2. Another - maybe easier - way of getting this achievement is to simply stick behind the rear of the car in front of your for the duration of the race. Simply do not overtake the car in front of you, just keep slipstreaming up and falling behind again.