First, complete the race n the shortest time possible, so you have a better chance.
Second, avoid all birds if you can. Getting hit once is OK though.
Third, try to pick up as many balloons as possible. Of course, they’re randomly distrubuted, so if the first 5 are right next to the trainer you’re probably screwed ^-^.
I still haven’t beaten it though…
Hitting one bird to get one balloon isn’t worth it, but if you’ll get 3 balloons then it is. And be careful particularly near the end of the course because there is an invisible border to the left, and if you try to cross it you’ll lose control of your chocobo for a while as it tries to get itself back on the course; I hit so many birds through doing this so be careful.