I had less trouble than I was expecting with these fights, even on 1999 Mode. I covered it in my 1999 guide, but I'll summarize here.
Lady Comstock takes critical hit damage from being hit almost anywhere, so critical hit boosting gear is very nice.
The Charge vigor, upgraded with the invulnerability option, makes this fight much easier. If you have Brittle Skinned as a gear option, the fight is downright trivial. Throw in a fully upgraded shotgun and the whole thing is over before she can summon her second set of goons.
- Hit her with whatever ranged weapons you have - I tended to bring a crank gun.
- When your shields are low, Charge her, which causes you to melee. This will activate invulnerability, plus recharge your shields. This also pops the Brittle Skinned bonus if you've got it.
- Unload your shotgun, and then fire off whatever else you can until your shields are down.
Once your invulnerability wears off and your shields are low, just Charge again. You could also retreat once the shotgun is empty, and reload your weapons and prepare to start from the beginning if that suits your playstyle better.
On 1999 mode, with around 5 infusion points into salts, I was able to take her down before I'd even halfway drained my salts or shotgun ammo.
The Charge upgrade can be somewhat expensive if you haven't saved your cash or prioritized it, but I didn't get it until just before this fight, and I just scrounged around the city, looking for enough change to afford it. There's a lot of ground you can cover in this area looking for resources.
You can use Vigors or set Vigor traps if you're having issues with her minions - Shock Jockey is pretty good for this. If you upgrade Charge with the explosive damage upgrade, you'll probably do pretty decent damage to them when you Charge anyhow. Bronco is my go-to crowd control option if things are getting hairy in close. When they're stunned, I believe they take additional damage, so if you've got a bunch of them on you, it might be useful to stun them to avoid wasting ammo.
You must fight her three times before she goes down, and I've listed the locations in my guide. It helps to go in fully loaded, upgraded, and healed, so knowing where she will attack can make a big difference.