On this page of our guide to BioShock Infinite you will find the third part of a detailed walkthrough of Chapter 30 - Downtown Emporia. From our walkthrough, you will learn how to defeat Lady Comstock for the first time. Her spirit will be the obligatory boss, and you have to fight her more than once. After winning the first fight, there will be another meeting with Lutece's siblings.
As soon as Lady Comstock has "risen from the dead" a new battle will commence. Lady Comstock has an unpleasant habit of bringing nearby dead people back to the world of the living and as a result killing standard enemies is pointless since she can resurrect them.
Focus your attacks on the Lady Comstock ghost and try to immobilize Lady Comstock's helpers by using Bucking Bronco or Murder of Crows vigors. Following this tactic should allow you to gain an easy victory and as soon as Lady Comstock is dealt with all of her spectre allies will return to the underworld as well.
Leave the cemetery after the battle, listening to Lutece siblings along the way. Open tears responsible for summoning ammunition or medical supplies if you need to, because you'll soon take part in new fights. You should also memorize the tears in case you need to return for the supplies while fighting your way through the Emporia.