I just finished the game on 1999 mode, and my complete guide to the difficulty level is here, but I'll summarize my strategy for the final fight:
My weapons were the Repeater and the Crank Gun. Both of these are plentiful where the enemies are, and that's where you're going to be. I never had to worry about ammo, as whenever I killed an enemy, I was getting more.
For gear, the critical bits were Brittle Skinned and Winter Shield.
From the generator area, if you face the window you jumped down from to get in, you'll see on the left is a rack of RPGs, with a crate of health and salt restoratives under it. On the opposite side is a rack of carbines and sniper rifles. In the middle is a few vigors that you probably already have, which you can take for free salt. Behind the middle console is a tear you can open for more health kits.
Down each of the sides of the upper deck from the generator are a couple of cover areas that both have a salt and health kit each.
You only win when the zeppelins have been defeated. The enemies will continue to spawn until you do so. Therefore, prioritize the zeppelins if you can. Sadly, these take the longest to down, and Songbird will be out of commission for a while if you ask for one to be attacked.
The rocket gunships have terrible aim. I let one stay at the end of the ship, shooting like crazy, and it barely scratched my core. It did hit me a few times though, which was a bummer.
Clearing the bridge is good for times when you're just being overwhelmed and your next target is a zeppelin.
You've got three types of enemies to worry about:
- Unarmored humans with repeaters
- Armored humans with RPGs
When a group spawns at the end of the ship, jump on the skyline and do a skyline strike on one of the unarmored humans. Then, unload your repeater (or whatever weapon you have) into him. Pick up his repeater, and off the rest of the unarmored humans. If you have Winter Shield, it should last you through the encounter with the humans. If not, you can use Charge with the invulnerability upgrade to restore your shields and give you a few seconds to recover/reload.
Meanwhile, the Patriots are making slow progress across the ship. You can Charge into them, or just whack them with the skyhook if you wish to engage the Brittle Skinned damage bonus. Then, unload with the repeater, or a crank gun if you have one already. In a pinch, you can use the RPG, but the small clip and long reload delay mean your DPS is going to be relatively low.
Once they go down, make sure no RPG guys have dropped near the core. If they have, Undertow them off the airship. If they're in close to the core, you might have to knock them down off the upper level, and then again to knock them over the railing.
As long as you don't let the RPG guys get in close and stay there, and you don't just completely ignore the Patriots, the core won't take that much damage.
At this point, you can restock health or salts, and regroup for the next wave. Target Songbird on a zeppelin if you haven't already.