To earn a Gold Star you must beat the Hunter Tutorial in 6 minutes.
This is a bit easier than the Monster Tutorial because there is more time. On a good run you can beat this in around 5 minutes. Repeat the tutorial a couple of times until you know it by heart. The hardest part is at the end when you have to fight the monster. Just keep shooting it with your Lightning Gun and Assault Rifle until it goes down. Always activate your shield when the monster is about to attack you.