This achievement is fairly difficult to write an exact method for, as a lot of the factors are out of your control. You may end up with someone who is only there to cause trouble, intentionally ramming your car for example.
However, there are a few tips that may help:
1) If you are playing against people with a low rank, they often make mistakes entering the first corner. Try holding back to avoid any pile-up that might occur.
2) Practise the tracks. This may sound obvious, but a good knowledge of the track and where to brake will ensure the best chance of winning.
3) If after a few races you're nowhere near the top, try quitting out and joining a different lobby. You may have more luck with a different set of players.