The description is a little bit misleading. You have to
WIN this race in under 3:03. If you get the second place with under 03:03 the achievement will not unlocking.
For me personally it was better to drive the long ways instead the shorter ones. Use your turbo as often as possible also in the curves and you will win a lot of time. I finished the race in 02:45:77 which was nearly 16 seconds under the requirement.
You can do this achievement during the main story visit or come back later whenever you want.