I try the following:

dont try and get the first balloon if it is on the left. If you try and cross the Champ, she will be ahead of you. I tend to stay straight, this usually cuts her off.

Dont hesitate to go out of your way, and avoid a couple balloons. Soetimes I stay to the right (on the lower level) and then when the screen turns again, I am in position to get more balloons, they see to be in a line.

Remember, dodging for a second, may save you a couple by not getting hit.

Its hard, but patience wins.