The objective of the mission is to collect all five checkpoints without breaking any traffic cones. Collecting the first checkpoint will start the countdown timer. The time each checkpoint adds to the countdown timer is 12 seconds at first, and for each consecutive record set, is reduced by 1 second until hitting the minimum of 6 seconds per checkpoint (in the original PS2 version, the time each checkpoint gives is always 12 seconds).
The reward for completing the mission is $200 for the first time, the reward will double the previous reward for each time you get a new record, and brings the player a step closer to 100% Completion. This is also the quickest way to make money, but there is a limit to how many times the player can complete it; realistically, the maximum money you can earn from Cone Crazy is either $838,860,600 or $1,677,721,400.