You should first do the event mastery skills relating to this mode (Hall of Famer achievement) to reduce the grind of doing 100 laps straight away. A star in every event is required for the Stars All Around achievement. You may want to focus grinding the long term skills whilst in this mode (backwards driving, 2-wheel driving, drifting etc).
Thunder Hollow Back Country takes approximately 40 seconds per lap when using shortcuts and turbo. There is also Radiator Springs Interstate Pass if you want a new track to grind. Jackson Storm is a reasonably fast car to use for these challenges.