Here is the full list of all 10 S.F.77 achievements.
Upgrade your weapon to shoot four projectiles at a time
Get two R-Shields that orbit your spaceship.
Upgrade your weapon to shoot three projectiles at a time
Upgrade your spaceship speed to level 5
Destroy the first enemy boss ship.
Upgrade your spaceship speed to level 4
Upgrade your spaceship speed to level 3
Upgrade your spaceship speed to level 2
Upgrade your spaceship speed to level 1
Upgrade your weapon to shoot two projectiles at a time.