I got this achievement by following the video below, using the same path.
The other Chocobo apparently can either finish at roughly 32 seconds or around about 38 seconds. The time seems to be random so this will be trial and error.
NOTE!: You can't win if the other Chocobo time is 32 seconds.
Keep running the same path and you'll eventually get 5 chests and win.
Edit: It does not matter if you hit any poles or not. Hitting the poles will only effect the reward you get.
Good luck and happy hunting!