I tend to play on Medium, so take these assorted thoughts and tips as you will:

* I think the briefing officer gives good advice here - use concussion missiles to take out some of the mines when you first enter the area, when you are still out of range (but only do this with the type A laser-only mines, not the missile-armed Type C's)
* Completely ignore the cruiser - there's too much going on for you to worry about getting it's health down - leave this to the transports.
* Clear out a batch of mines first before calling for reinforcements, that way when they arrive to lighten the load, they won't get destroyed in a hilariously quick time.
* Use your wingman to cover you when you start getting hassled by fighters, and only engage them when you have a shot of opportunity, or are taking too much of a beating.
* Remember that bonus goals exist for clearing out each section of the minefield, if you are after a super high score.
* Taking out the mines early on makes things easier when you get to the point of disabling the shuttle and dealing with the transports. Personally, I disable everything (helps with efficient power management, by alternating between regular and ion cannons) so that nothing escapes, and then get back to destroying everything later.
* The mines are sufficiently weak that disabling them is, imho, a waste of time unless you're doing it to conserve main cannon energy. You'll be getting shot at by fighters the whole time, so if you want to come back round to destroy them later on, you'll still be taking a fair amount of fire. Also, unless you're being methodical and targeting each of the mines in turn, you won't know which mines you've disabled and which are still active.
* I tend to use ion cannons when dealing with the fighters, and save the main cannons for the mines, or for redirecting energy to the shields.
* Go to full power on cannons, and keep transferring most of the energy to the shields, leaving only a few shots in each of the banks at any one time.

I have to agree with the above!
I used most if not all my missiles on the mines.
I preferred shooting the mines that can launch missiles at me as well.
Because the long distance you can shoot the missiles down.

Definitely what was said above. Your task is to clear a path for others to take out the capital ship, not engage it directly. That said, use "stand-off" tactics and your missiles to clear the mines. Stay out of their range for as long as possible. Don't go wading in, at least not at the beginning. Once the evac starts, then you go after the shuttles and transports.

What I did to beat it was I packed Torpedoes and dumbfired them all at the cruiser Lulsla right at the start. That'll take out about 50% or more of its shields which makes the job easier for the incompetent TRNs Sigma and Omega.

After that, focus on the enemy fighters. If you keep them busy they won't go for the TRNs and the cruiser goes down faster. Be aware that once you clear them, another wave of X-Wings will launch from the Lulsla.

I gave up on specifically going after mines, but it helps a bit to get the ones in front of the Lulsla so they don't hassle your TRNs and their torpedoes. If you do go for the mines, go for the star shaped ones and not the shuttlecock ones, since the former fires a lot more and therefore are the greater immediate threat, and the latter spits out a missile when you splash it which is tough to deal with when you have other things on your plate.

Once all the shuttles launch, go straight for the Lambda shuttles instead of the TRNs, and disable the one with the commander in it. Destroy the rest. If you wait too long to do this the Commander might get away.

Once your missiles are all spent, set your Lasers and Ions to linked fire. Then if you hold W while firing you fire off Lasers and Ions both at the same time, effectively giving you twice as much DPS against shields. This is a good way to quickly take out the shuttles if you're under attack by other things

Once the cruiser and all the shuttles are destroyed/captured, you can go clear all the mines in peace if you want the bonus points. Just be careful that the shuttlecock looking ones fire off a missile when you destroy them. Usually though, if you hit them with a linked fire shot your second laser destroys the missile as soon as it launches!

On hard my wing men die there are no reinforcements and the transports din too. I don't have the luxury of missles. I need something that can damage the cruiser.

This mission really isn't too hard, but may take a few attempts. You should really equip your ship with Heavy Rockets - they are faster, more predictable and less prone to getting shot down.

When first entering the system, try to take out as many (maybe 8) of the standard laser mines with your lasers as you can. This will ease up a little of the cross-fire when dog-fighting near the Cruiser. Be careful not to accidentally attack the Cruiser.

Break the attack on the mines to engage the new ships as they deploy. Destroying the 3 A-Wings is a priority since they have missiles. Try to steer the battle away from the Cruiser and the mine field. Once the A-Wings are gone, cleaning up the Y-Wings and X-Wings shouldn't prove too difficult or time-consuming.

While you're off dog-fighting, Imperial transports will attempt to destroy the Cruiser - they will fail. But they'll knock the shields down to about 50%. Once all the starfighters are destroyed (or before the Cruiser enters hyperspace, which ever comes first), turn to the Cruiser and start firing the rockets. Even if the Cruiser is firing at you, a little maneuvering during your approach should allow you to release your payload no prob. Maybe 4 rocket hits are needed to drop the shields. Once shields are down, disable the Cruiser with Ion Cannons. Maybe only about 12 shots are needed.

Once the Cruiser is disabled, and the enemy starships destroyed, the mission is pretty much over. At this point, make your way to destroy the rest of the mine field. Once the mines are cleared, start to take down the hull of the Cruiser. Once it's at 50% hull, it will deploy 4 transports and 2 shuttles. Destroy the transports, and disable the shuttles.

Then finish off the Cruiser. Let the transport that jumped in to capture the shuttle finish its mission and... Viola! All bonus objectives completed. Happy Hunting, and Good Luck!

My issue is the shields haven't been coming down at all because the transports are getting destroyed like cannon fodder.

This mission is virtually impossible because my wingmen are COMPLETELY incompetent, unless I've already downed the cruiser's shields... at which point they fire their heavy weapons and steal the kill away from me. This mission would be easy if my wingmen would simply fire their heavy weapons at range instead of stupidly entering into knife range and killing themselves. Meanwhile all the rebel fighters are going after me and only me. WTF are those stupid ***** doing to kill themselves when I'm the one taking all the fire? I only barely managed to kill the cruiser myself on my own, and I had to abandon all the other objectives to manage that. Literally all my wingmen died and I only got to kill the cruiser.

Have any mods been made which corrects the AI's pathetically suicidal behavior? Or for me to take control of my wingmen so that I can fire their long-ranged weapons for them? I don't need reinforcements, I need wingmen to stop being suicidal.

I always get the impression that these games weren't really tested on hard mode, even in X-wing Alliance on hard many missions become impossible because the difficulty level also makes your wingmen literally braindead and makes the enemies superaces.
Similar case in X-wing vs Tie Fighter and it's even worse in that many missions are balanced with humans playing in co-op in mind so in many cases your wingmen aren't up to the task even on medium sometimes.

This is an old thread but this mission is impossible for me. I did every previous mission without dying once but I've been doing this for over an hour and have only once made it anywhere to close to the end. I feel like I must be missing an important gameplay element or something because I have died about fifty times so far.

Well time to read all the manuals and come back an ace pilot.