According the official strategy guide:

In order to win the sun sigil, you'll have to complete the race in under 0 seconds! How does this work? Let's imagine you reached the finish line in 35.9 seconds, having touched a bird. This means that the 'interim time' is 38.9 seconds. However, you also caught 13 balloons, so 13 x 3 seconds are deducted from your result. thus, the final time is 0:00 seconds.
P.S. You need to hope you're feeling lucky.
P.P.S. And pray.