This mission worked out fine for me, I started the mission with no attacking frigates, but 4 carriers, so you can build up your frigate fleet as soon as you get in here. I didn't get too many BCs here. I also had 2 DFF, and 4 marines in this one.
I have some probes built in the last mission already, so send them out and below the horizon, or they'll get destroyed. Basically cover the front and the right of your MS.
I built some, about 5 flaks, and the rest torps or ions.
Then I built 15 ion plats, 5 gun plats, and used my DFFs to cover them up. Put the plats about half way between you MS and the enemy resource.
Wait for the first wave of enemy, and this is the worst one, make sure your ships don't go too far beyond your plats. Activate DFFs only when a destroyer+ ship comes in.
Use your marines to capture the enemy BC coming in at the right of your MS with some DDs. Use bombers to take out DDs and the heavy missle module on BC, then capture it. I then scuttled my Vaygor BC captured in M09. The newly captured one should have a hyperspace inhibitor on it, if not, then capture some other ones. This will be useful in M13.
I basically waited until the enemy is no longer coming. I think they ran out of resource since their command center is not even produing fighters anymore, and I guard the resource in front of my MS too good that they can't get anything.
If you ping the battlefield and see nothing produced/coming anymore, (Usually after the death of Makaan) then you can go ahead and clear out the BC fleet in front of the command center (1 BC), the shipyards, and send in marines to complete the mission.
Retire all your frigates for the next mission!