Alliance Intel needs to know what the main fleet in this sector is, so that we can work on making our escape. This means an A-Wing and a recon mission past a bunch of Imperial capital ships.
The main trick here is to fly evasively to evade the heavy fire coming from the various Corvettes, Battle Cruisers, and Star Destroyer. Get close enough to make your inspection, then move on to the next target. Use the A-Wing's speed to keep out of too much trouble.
Once you've inspected all the major Imperial craft, a few of them will launch probe droid capsules. By this time you've probably got some enemy fighters chasing you, so keep evading, but fly towards the various probe droid launches and destroy them with guns. Don't go for a missile shot, because the amount of time you have to hold still to get a lock will probably cause you to take a bunch of hits.
Once the probe droids are destroyed, it's time to go. Dogfight whatever fighters you need to to make your escape, or you can always try your luck at killing a few of the capital ships for bonus points.