This refers to the 'Instant Missions' which are separate from the main game. I recommend waiting until you can at least buy the 'Decimator' then once you have it upgrade it a bit.
With a decent bike press the
button and select 'Instant Missions', scroll along to 'Arcade' and press
to do the 'Subtroit Arcade'.
All you do is race through the 18 checkpoints, each of which give you more time, and win the race. The achievement unlocks immediately.