Unless you are in a top car like Red Bull, McLaren or Ferrari (which you cannot start your career with), this Achievement will be fairly hard to attain without "cheating" this year. Even with the A.I. set to Professional difficulty - one below the highest difficulty "Legend" - and pushing it to the limit you will not end up in the top three with a mediocre car.
If you want to get this achievement as fast as possible without the career experience of starting out in a mediocre car and working your way up to a top tier car, simply dial down the difficulty and settings by selecting the track you are currently at in career mode via the paddock - you will then be automatically taken to the race options screen.
Select "Difficulty Level" and make sure to scroll down and change A.I. difficulty to Amateur. This should enable you to finish in the top three with any car.You are allowed to use driver assists and simulation options (tyre wear, rules and flags, fuel sim).