For this achievement, you need to win the Drivers' Championship in Career mode on any difficulty.
Before starting career mode, I highly suggest unlocking either Sauber or Lotus via Young Driver Tests. These are the best two teams you can start your career with (I personally preferred Lotus but I believe these two teams are pretty similar). I'm sure if you're amazing at F1 games you can get by with using any team, but if you're like me and have never played one before, I would highly recommend using Sauber or Lotus.
Set the difficulty to easy then adjust the driving assists to your preferences. If you are half decent at racing games, you should be able to win most if not all of the first 10 Grand Prix. (I won 8/10 of the first two and came in the top 10 in all 10) I would say I had about 230 points. After the 10th grand prix, one of the top three teams (Ferarri, Red Bull, Mercedes AMG) will offer you a contract. With any of these cars you should be able to obtain pole position and win the race with little difficulty. If you win all your races after you accept your new contract, you should unlock this around the Korean Grand Prix (At least thats what happened for me).
If there's any way I can improve this let me know.