Very frustrating but ultimately not that time-consuming. The AI for the opposing chocobo can take a "fast" or "slow" route. It tends to take the fast one most of the time, and it makes this achievement impossible for that attempt. It's pure RNG, and there's nothing you can do. Even when it takes the slow one, your movement has to be tight, you can only beat the opposing chocobo on the slow route by a matter of inches.
One thing to keep in mind is that hitting poles does not matter for this achievement. It does effect the quality of items you receive, but it's nothing worth worrying about.
The route is as follows:
1) Simply go forward for the 1st chest.
2) Take that immediate right and go backwards for the 2nd chest.
3) Take that same right and go forwards for the 3rd chest.
4) Simply go forward for the 4th chest.
5) Take the 2nd right and go forwards for the final chest. You need to land in front of the other chocobo or he will body-block you in second place. If he took the fast route, he should already have won by the time you land. If he took the slow route you need to land in front of him or he will body-block you in second place and your movement wasn't quite clean enough.