Bioshock Infinite

[Kreekakon]

How do you kill the siren before she resurrects someone?

If you're trying to enforce that rule down to the letter, then it's basically impossible as there's always going to be a bunch of bodies around, and the Siren is just too meaty to kill that quickly.

You can however prevent "bodies" which have been resurrected to be brought back multiple times by killing them with things like fire, or lightning. Those type of damage will destroy bodies upon their death, and the siren will not be able to bring them back for another wave.