After triumphing over the Breaker's Bow challenge pretty quickly, I was feeling pretty proud of myself...only to get shot down as soon I got to the Trapper Shingle. In this room you have to use your Fang Repeater to shoot down small targets that appear...while running away from the collapsing floor. I can't seem to get the second place prize here, even with the repeater upgraded to hold 14 shots; as soon as I reach the last row of balloons, I don't have any time to fire shots because the floor starts falling too fast.
How do I improve my score here and win the first place prize? Are there certain upgrades I should be getting?