FWIW, never have bested Catcher Chocobo enough to win the Sun Sigil. I'm lucky to do well enough to pick up Caladbolg itself. Never have needed that weapon again Sin. If you have the burr under your saddle, good on ya and best wishes, go get 'em, but you really don't need it.
Yes, you can attack chocokind rather than capture them, especially at that point in the story with their Choco Meteo, argh. Defeating one means being right quick with a massive attack, though.
Guides and other contributions: http://www.esque.com/slr/gamefaqs/ FFX, FFXII, KH, KH Re:CoM, KH2, Okage: Shadow King, Secret Agent Clank
Yeah I spent a majority of yesterday trying to get it and basically you need to be pretty lucky with the balloons during the first and second stretch otherwise you're not going to get it because the birds in the second stretch spawn too awfully for you to try to pick up balloons on the left side without getting hit by a bird.
You also need to stay ahead of the trainer because not only does she mess up the path you can safely take to avoid the birds by forcing you to avoid the birds in an unfavourable direction and she also gets the balloons you need.
Then the key to dodging birds is as follows; do not try to preemptively dodge because they track they have tracking the whole time and do not be afraid to go completely left or right to avoid them. During the first turn you want to be going towards towards the left boundary and then a little Before they hit you you want to take a sharp right until all four birds are gone, then you want to stay near the right side of the boundary till about halfway where they start spawning from the end at which point hopefully you can nab one or two balloons while again heading towards the left boundary and taking a sharp right just before the birds hit you; the game might try to bait you into taking a second too late before you dodge a bird so don't take the bait because a balloon might shave three seconds off but a bird adds three seconds and stuns you for one and a half so it's definitely not worth the trade.
Then during the third stretch you want to head towards the opposite direction of the balloons staying near that boundary so that when the birds spawn you can easily avoid them in the first half. Then on the second half of the third stretch you can dedicate most of the second half towards the balloons and then dodging away from them.
This is assuming you never made contact with a bird btw, but I practiced this path until I could get it 10 times in a row without touching a bird and then just kept going until I got a good balloon placement on the first and second stretch. My final time was 35.7 with 14 balloons and 0 birds so you know it shouldn't be too hard knowing that you can completely overkill it.