Charge with shield recharge/temporary invuln. upgrade is incredibly helpful for this part, while this might be more for 1999 mode since you're shield recharge is longer and must be managed, it should be helpful on every difficulty. Undertow is also useful as most enemies here put themselves in a vulnerable spot to be knocked off the airship. This of course leads me to suggesting Blood to Salts to keep your vigors sustained.
The only other big suggestion I have to make is to manage Songbird according; don't summon him for nothing whenever the time is up. Use him on arriving zephyrs that are still full of enemies and such, or when something is damaging the core that needs to die immediately, but if you use him on an circling zephyr that just has a lone patriot on it, it's really a waste.