There are checkpoints throughout that final fight (thank god). At least 1 checkpoint. It seemed (to me) that you lost money when you die, however, if the ship blows up it reverts you back to the total money you had at the checkpoint. (At least as far as I could tell). I ended up having 7300, meaning I could have died 73 times.... so it really was not an issue for me.
I must have "restarted" the fight (which it does on its own when the ship blows up) around 8 times. I died multiple times during each one of those fights. The strategy that seemed to work best for me, (I tried this the last time or two, which made a pretty huge difference), was to use the skyhook.
Equip gear like frost armor (invulnerable for a few seconds after jumping off sky hook), and the fire one, that does AOE fire damage when you dismount. You can also equip other armors if you have them that help with this. (I kept armor on that automatically reloads free bullets 40% of the time). So skyhook + dismount to 1 shot the normal guys. Each time you dismount your invulnerable for 4~ seconds so you can pop some shots off on the patriots etc. Rise and repeat. I kept the shock vigor on to shock the patriots and then the handcannon or sniper to pick their heads off. If you shoot the same spot the head was (a little lower) it will still do crit damage.
Make sure you focus the songbird on the gunship (that has a huge Gatling gun) before targeting the Zeppelin. The gun ship (seemed) to do more damage than two patriots. I have read you can leave one of the enemies on the ship and it will not respawn another wave, though I did not use this strategy.
You can also use the songbird to clear out enemies on the deck. It's timer is dramatically reduced when you do an attack on the deck so don't be afraid to use it if you have to.