Definitely possess Rocketeers. IMO using that ability on Patroits is a waste, though--it lasts about 5 seconds on them. Return to Sender is good against those, or just spam Shock Jockey a few times as you unload into their backside with a Crank Gun. Using the songbird to clear the deck of Patroits is not a waste even though it doesn't look objective-y like the aircraft, but clearing the smaller transports out usually is.
"That is why war is so tragic. To win means to make victims of your opponents and give birth to hatred." - Kratos Aurion, Tales of Symphonia
Possess Rocketeers, use Songbird on ships that are firing on you or just coming in, and stay close to the fight. You will undoubtedly lose and have the ship health hit zero if you hang back, if you get into the fight you kill faster and also give them another target to hit besides the ship.
So, Patriots are the main targets for flat damage (if you move to the front of the ship fast you'll probably end up behind them, and do extra damage), Rocketeers are huge for Possession (but any targets besides Patriots are good, as it's basically a kill plus extra target plus extra damage for very little salt), When the main groups are down jump up on the wire and refill, and also look around for random guys.
Songbird should be for the blimps almost entirely, unless you get overwhelmed and two patriots make it to the platform, then it may be worthwhile. You can take down the ships with a few RPG blasts if he's on Cooldown, just don't let the gunships get too much damage going.
I hardly ever use vigors. So I'll need to get used to using them. I was hoping I could hang back with a sniper rifle and Elizabeth could feed me ammo. But this obviously isn't working. Thanks for the tips, guys.
I had a hell of a time with this on Normal my first time though, but my second time though I had little trouble using a full upgraded charge with the Burning Halo gear on just about everything. I did use Possess on the Rocketeers and used Songbird to clear everything from the sky. Upgraded Shotgun and Handcannon to do damage to the Patriots after charging in. Undertow also works well on them.
use songbird on the huge ships as soon as they turn red. If they're not yet vulnerable use the bird on the firing ships while you take care of the ground. Use the vigor that converts enemies into allies that way you're not alone in the fight.