Well it is a bit of a handful. I believe on my first play through I used the F-15, and I think I ignored the tunnels. I can't remember the SP weapon I used, but anything ground attack should work. Using rocket pods is actually surprisingly effective. You really only need to deal with helicopters and Harriers, everything else is on the ground.
Now I like to stick with the tanks and give them cover first, then I work on that operation to knock out the supply in the canyons. Working with the helicopters to take out the internal base is really something for people who have played the previous Ace Combat games and who are used to flying in small tunnels.
I would recommend that once the mission moves towards the fortress itself, to go for the anti-air targets with your missiles in quick high speed passes. Unless you are playing on the hardest difficulty, you should have missiles to spare.
Also, don't forget to use that attack assist thing where you press and hold up on the D-pad. Make sure there are a lot of targets in front of you to get full use of all the fire power. I hope these brief pointers help.