Sonic & SEGA All-Stars Racing

For this achievement you will need to accumulate 300,000 miles over the course of the game.

The quickest way i found to earn Miles is to setup a 1 lap race on Whale Lagoon, i dont think the racer matters but i used Sonic, each race you should earn 2,000 or so miles COMING FIRST. There is a chance to earn more Miles each race, by finishing the race without collecting any power-ups you'll earn an extra 250Miles and by finishing the race without drifting you'll earn an extra 250Miles (Thanks to drabik for those)
Now once you have won the race and it is over you will be brought to a menu screen, select "Play Again" and do another race over and over, it all gets saved.
Note: if you fall of the track during your lap you will lose 300miles off the total earned, not much but still annoying

The reason i say 1 lap is i noticed that for 3 laps i got 2500ish miles per race, so if you can get 2000 a 1 lap race thats 6000 for 3 races, which is more than doing one 3 lap race.

Hope this helps speed up the process.
You can check your mileage by viewing your licence from the main menu

This will obviously unlock the lower level licenses and their corresponding achievements....

Here's a video showing the method (Note i pick up one power up making me miss the extra 250)

there is a easier way and all u need to do is pick a motorbike on time trial on beats showdown lvl n just keep the throttle down and each 30mins is around 15,000 or 20,000, u dont need to steer as motorbikes are quicker on recovery and that lvl has hardly no hazards on it