Sonic & SEGA All-Stars Racing

For this achievement you will need to accumulate 750,000 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 more automated way to get this achievement (and all of the other related achievements).

Go into Time Trial mode, pick any racer, and select the Icicle Valley track (it's the second track in the list). Find something to hold the gas down (you will probably want to change the controls so that A is the gas) and go get a sandwich. The car will drive itself around the track; whenever you hit a wall too hard or fall off the track (should only happen on the final jump on the track) it will re-adjust you to go in the correct direction.

You will need to check on it every hour or so (as the car either gets stuck grinding a wall too fast to force a reset but too slow to finish in time or the game just ends), but you can make up the 250,000 miles needed between silver and gold in a few hours without doing much.

The fastest way in my opinion is to start the level "Treetops" with 1 lap and no hazards. I had about 200 000 miles left when I had gotten most of the achievements and doing this method it only took me about 2 hours. You can easily complete the level in 35 seconds earning you about 1900-2000 Miles everytime.

Ok, so i started out with Spilners guide, and to me it feels like it could be quicker, so here is a vid that i am using which i feel is less time consuming, this isn't my vid so props go to whoever came up with this originally, also, rather than taping my trigger i put a rubber band around the trigger, to the right stick and sat the controller, plugged in, on a pillow so the vibrations didn't annoy me, anyways, good luck.