Astrobatics/Techniques

Super shot special usage (Asteroid and Mine levels)
The super shot in Astrobatics can be performed by not firing for a while and letting the blue bar on the top part of the screen charge as mentioned by Basic mechanics, aside from being good to use on weak enemy hordes, the super shot is good to use against cannons inside an indestructible asteroid found in Missions 3, 8, and 13, you just have to aim at the center where the cannons reside, the super shot is also good in destroying mines, which is found mainly in missions 9 and 14 (there are probably more, but mines debut on as early as Mission 4), this will help save your Laser in clearing the mines, but take note that you will be vulnerable for a little while when you try to charge your shot.

Power-up special usage and receiving efficiency
This is a combination of several minor techniques all at once, for one, if the level gives you a choice to pick either a Weapon Power Upgrade or Rear-shot/Spread Fire/Turret, ALWAYS take the latter first before you take the Weapon Power Upgrade, this will allow you to increase the firepower of both your Rear-shot/Spread Fire/Turret with your main cannon more efficiently as this means you need less Weapon Power Upgrade power-ups to get before you reach maximum firepower, second, the Homing Missile and Laser have other uses aside from just destroying enemies, Homing Missile can be used to protect yourself from enemy fire as the missiles have a hitbox too just like the green homing missiles you take down that come from enemies, this also means Homing Missiles can destroy Mines, Lasers can also be "panned", basically move your ship upward or downward then fire your Laser, but this is only effective in destroying weak enemy hordes and clearing out mines, Laser can also be used to shoot the cannons inside the big indestructible asteroid in Asteroid levels, but requires accuracy in doing so.

Weapon Combinations (Support Airstrike + Homing Missile, Super shot + Laser)
Certain weapons can be combined to have a more desired effect, for example Support Airstrike can be combined with Homing Missile, once you activate Support Airstrike and the ships come in, you can fire Homing Missiles along with them to have better damage output, Laser can be combined with Super shot to further augment the damage of your Laser, and finally Mines work better in taking down rear enemies when combined with your rear cannon.