Make sure you've gone through all of the levels in the game. It's not necessary to beat the game, but you have to beat all of the Act 1 and Act 2 levels in the game so they are unlocked in Ranking Attack Mode.
Once you have them all unlocked, quit to the main menu. Scroll down under Continue, and go to Xbox Live. From this menu, select Ranking Attack.
Now all you have to do is play through all the levels again. You must finish all of the Act 1 levels as well as the Act 2 levels for the achievement. There are no lives on Ranking Attack, and it does not matter what your time is, just finish the levels and you'll get it.
This is more tedious than challenging, but at least it will get you some practice for the S Ranks. Good luck!
Note - It seems doing the levels out of order may delay the popping of the achievement. If you do the levels out of order, apparently quitting out to the main menu, going back into Ranking Attack mode, and doing Green Hill Zone Act 1 again will make the achievement pop.