Just thinking here....
Are you trying to destroy the big ships or the fighters? The basic fighters in the easy missions should only take a couple of hits to kill. A frigate on the other hand, you can only kill the turrets most of which are a bit harder than a fighter, the main turret on the front is significantly harder to kill. You can also take out their engines with a bit of effort. On Destroyers and up, you can only really take out turrets and shield generators (if they have them, in which case they need to be taken out first).
Frigate has four turrets at the front, two in the middle, two at the back as well as two other targetable areas that I've never killed.
Destroyer has three rows of four turrets on the top and the same on the bottom, I also seem to remember a cluster of four turrets amidships on top. can also have four shield generators on the back part of the topside, also has a bridge, which again I have never been able to destroy.
The Bridges take quite a few missiles to destroy. I have not counted the quantity needed but it is a lot. In fact it takes the most out of everything else. I think even more than the Antenna under the Space Stations. If anyone plans to take out the Bridges they really need to make sure and get the Missile Upgrades so that they have enough missiles to do so and still finish the rest of the mission. At least that is my suggestion.
I heard it was easier to take out the Bridges with the Proton Torpedo but I have yet to get that to test it out. Once my Smuggler hits 50 I will try it out.
Note: For the new players that may not know. If you use your lasers on the shields and bridges, you are wasting your time. They can really only be destroyed by missiles. You notice which targets require missiles as they flicker with light blue and/or white circles around it as you hit them with lasers.