Update - As per SpeedBumpVDrop's comment, this achievement is discontinued. :(
Fairly easy achievement, but has to be earned online (as far as I know).
The short of it? Grab a friend, have him take you out. This can be an aggressive take out, to him tapping you and you purposely slamming into a wall. As long as it registers as 'Player A' took you out and focuses on their car you know you'll have done it right. Then just return the favour.
Of course if there is people still playing online the same principle applies, get taken out by somebody, catch them up and dish out some payback in the form of a takedown! This will be easier with beginners as, when I was playing this online a while back, the pros tend to fly off and almost become untouchable.
Any feedback just drop a comment :)