There's one or maybe two exceptionally "high opportunity" streaks they feed you out of however many there are in the pattern: this is that minus 10 misses and 2 hostages. He's turned up three or four times now I think; maybe the game starts to feel bad for you after a while.
The only real trick is that you don't use the red dot, you use the sights on the gun.
Well... looking at the clock, I've now officially used over an hour of my life on this. Thanks Critic.