This is a relatively an easy achievement as the course of your career or any disciplines, you will be overtaking a lot of drivers during your race and probably end up having this achievement without even trying! (This happened on my case)
Note: You can obtain this achievement on any event.
To "slipstream overtake", you need to get close behind a car in front for a bit longer and overtake without making contact.
Once you have successfully overtake, you should see Slipstream Jnr. Icon appear on the left of your screen which means you slipstreamed past a driver and therefore Achievement Unlocked!
Note: If you are unsure if you have succeeded, then choose a Red Bull Driver (Sebastian Vettel or Mark Webber) as Red Bull inherits you "slipstream boost bonus" every time you perform a slipstream.