You will need to complete the 13 series races and all 5 showcase events in The Domination Cup
Each series consists of six races. You must complete each race, although you do not have to win the race or the series. But you do have to complete every series and get the required amount of series points (the blue slider at the top).
You also have to complete each showcase. The only time consuming one here is the endurance event (Le Mans 250) which will take approximately 2 hours depending on skill.