There is a hint in the instructions for Invasion Anarchy relating to the bonus game, but it is pretty cryptic so I am making it clear!

When playing the game in normal mode, if you can "shoot efficiently" or conserve your bullets by not missing the aliens for a while you will receive the "ribbon of proficiency" (next to the shields) after scoring about 1200 points

Achieving the ribbon is no easy feat, but when you have it, instead of the game ending when you are either captured or bombed you will get to play the bonus round which is scaled to your current level, and if you survive the bonus round you will receive a new starship to continue your game (and there are 4 different starships available).

Once you have the ribbon you can stop conserving ammo and blast away!