I got this achievement by playing by arcade rules in original mode. Try to pick up as many customers as possible to make sure your time doesn't run out.
When your delivering your current customer to the place he or she wants, try to place them next to your next customer, so he can step right in. This gives you 5 to 8 seconds extra time!
Start with green custumors. They pay much. If you don't see then close by, then just pick a orange or red one. The time between customers is the most painful, so try to avoid them.
I got this achievement after earning $5,019.94
Other achievements for lower licenses do not unlock when reaching the S-license.