The Dogfight scene is directly after the Junk/Garbage/Trash compactor kind of scene. I don't think there's any specific way to guarantee the scene will play, but when it does it's not any harder or easier than other scenes.
Some prompts will be you avoiding fire, other prompts will be you shooting the alien ships down. Even if you game over you can still continue and it will just put you back at the start of the scene again, like the rest of the game.
Just make sure to be playing on Ace difficulty!