All right, obviously I'm doing something WRONG... I've slowed the game down, but the cross-hairs and space bar do not respond fast enough to shoot anything down. And you can't finish the game until you do.

(And I mean the tracking does not even engage until the target has buzzed around a bit and by the time you're even moving the cross-hairs toward it, it zooms out of range.)

What's the trick?

Just keep trying, it took me ages to get it aswell.

The trick is to set the ship to attack speed before doing this.