Crazy Taxi

Has to be done in Arcade mode.
The License achievements do not stack, you have to get an S, A, B and C rank on seperate attempts.
The licenses are split by the money you make

S = $5000+
A = $4000-4999
B = $3000-3999
C = $2000-2999

To make this even easier you can go into settings and increase your starting time and lower the traffic difficulty and this won't affect the achievements

I got this achievement by playing by arcade rules in arcade 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 $5,083.16

Other achievements for lower licenses do not unlock when reaching the S-license.

Just adding to the previous solutions, you will need $5,000 or more to obtain this achievement. But, here's my share.

Tips:

Crazy Dash: Press the button to have your car in reverse. Then press the to have your car on drive. Right as you enter drive, hit the to accelerate. This will perform a crazy dash. There's a Challange 1-1 of the crazy box that will help you understand this move better.

Crazy Drift: if you press the then right after another and hold, your car will slide. This move gives you points and also allows you to make sharp turns.