When you're on the results screen, where it tallies up your score and displays your rank, use Sonic to jump into the rank letter multiple times to break it.
You need to break letters D, C, B, A and S throughout your playthrough for this achievement to unlock.
If you want a guaranteed D rank in the stage, choose Sweet Mountain Act 3, and leave Sonic standing still until it comes up with "Time Up!" on the right side of the screen (after 4 minutes), then finish the stage. You will finish with 0 points that way.