Austria has a low number of turns and is commonly the easiest to get a good lap time. Mercedes, Ferrari or Williams are the best cars to choose from. I find the Williams the easiest to control both braking and accelerating.
After leaving the pits, change your Fuel setup to a mixture of Rich. This will give you the best performance, and help you to get the fastest time.
You can use mid-session saves. If you perform the turn poorly, load your save. After performing a great turn, save and work on the next turn. You need to be in at least P15 at the end of the qualifying session to move into Q2. Doing this 5 times will get your the achievement.
If after 5 minutes of qualifying, you are still holding at P15 or better, then you likely won't be overtaken. You can save and speed up the time, to reach the end of qualifying if you don't care to get a higher position or improve your time.
It seems to take 5-6 minutes to update the counter in the achievement. Repeat this 4 more times and you will have the achievement.