Space Quest III: The Pirates of Pestulon/Space Battle

Strategy

Make sure you're switched to Attack Speed (Main Computer menu option 6). Configure your global game speed to one that suits you (this guide recommends 6 or slower). Enter the Weapons Systems menu 8 on your computer to commence the fight.

Pay close attention to your radar. Enemies may be "In Front" or "In Rear." Set up your shields accordingly (i.e. F for "In Front" and B for "In Rear.") The game always alternates between front and back, so you can "flip" your shields immediately following an attack.
Enemy ships attacking "In Front" can not be targeted.
Every "In Rear" attack will give you a chance to destroy the enemy ship. To get a lock on, simply follow the ship with your cursor using the Arrow Keys. Although the ships will attempt to move out of the way, there is no clever strategy here.
Destroy four ships to finish the game.

Controls

The controls are painfully simple: F sets up the Front Shield, while B sets up the Back Shield. Once engaged in combat, use Arrow Keys to move the cross bow cursor to target an enemy's ship and use Space' to shoot.

Speed

As is the case with almost all 'arcade' sections of the Space Quest universe, it may be of help to lower your speed setting. As is the case with Astro Chicken, it's generally a good idea to keep it around 6, although the value may depend on the performance of your computer (or the settings of your DosBox).

Bottom Line

This is a very simple fight, and it should not take much of a learning curve to master. The only real "challenge" of this minigame is in tracking of the enemy ship, apart from paying attention to shields. Assuming your speed is set to a reasonable level, this game is trivial.