To earn this achievement, you will need to complete every series (13 total) and every showcase (5 total) in The Forza Driver's Cup
At first, only some of these will be visible. Once you complete the Driver's Cup Champion achievement, the rest will be unlocked.
Each series consists of six races. You must complete each race, although you do not have to win the race or the series. However, you will notice a blue slider bar at the top of the banner showing your progress towards 110,000 series points. You need to do well enough to complete every series AND have at least 110,000 series points. But just getting to 110,000 alone isn't enough.
If you managed to reach the Forza Driver's Cup, you will already have a good idea of what level of drivatar difficulty you can consistently do well against.
You also have to complete each showcase, and you will be rewarded with a free car for each showcase completed.
The main obstacle to completion, other than time, is having the credits to purchase the cars required to run each series. These generally require high tier vehicles, which tend to be pricey.
I was at level 90 when I got to the Forza Driver's Cup, and I had almost always chosen a greatly discounted (or free) car for each level reward. This meant that I already had cars that qualified for 12 of the 13 series. But I still had to shell out 1.5 million credits for the Renault R.S.17 grand prix car. Ouch!
Besides the achievement, you will also earn a sweet car and very cool driver gear. Have fun and be ready for a time investment.