Your last challenge will be to protect a generator responsible for powering the zeppelin. The Vox units will be arriving in waves and aside from simple soldiers you'll also be dealing with automatons (thankfully you won't encounter any new Handymen). The current technical state of the generator is represented by a blue energy bar located in the upper right corner of the screen and if the generator is destroyed you will have to restart this entire battle. Thankfully you can find a lot of weapons and ammunition on the deck so don't worry about conserving your supplies. You can also locate some salt in the area and as a result you will be allowed to use vigors more often than usual.
The game will allow you to designate targets for the Songbird, however the bird will need to rest before the next attack and that recharge period is represented by a timepiece seen under the generator's energy bar. Use the Songbird as often as you can, ordering the bird to attack airborne targets or enemy troops on the zeppelin's deck.
There's a sky-line above the deck and you can use it to get to the top of the zeppelin. You can find some tears at the top, containing medical supplies and a sniper rifle. This is a good spot to attack your enemies from a safe distance and to issue orders to the Songbird, because you will be able to see the entire deck from here.