Field of Honor Mission
Destroying the larger Orion Capital first will cause the smaller one to flee.
Go back and replay missions to earn upgrades faster.
Try to fly up behind a starship you're attacking and pull up beside an engine. Concentrate your fire on that engine. If done correctly, you won't get hit while destroying the starship.
Destroy "Akula" Class Starships
Disable its shields, then go directly in the middle to the impulse engines and fire at the ship.
Destroy "Orion" Starships
You do not have to destroy both Orion starships, just disable the shields on each ship, and they should warp out of there.