WARNING: The following article contains spoilers for Batwoman Season 1, Episode 19, "A Secret Kept From All the Rest," which aired Sunday on The CW.
In the penultimate episode of Batwoman's first season, Alice got a hold of a translation of Lucius Fox's journal. While Lucius had encrypted his entries, Alice finally got what information on how to take down Batwoman. As it turns out, Lucius' journal contained details on how one could potentially take out Batman, and Alice plans on using that very information to get rid of her sister.
However, the big surprise came when it was revealed the first part of Lucius' plan somehow involves Kryptonite. The radioactive green mineral hails from Superman's home planet Krypton, and it's widely known to be his (and Supergirl's) greatest weakness. And yet, Lucius Fox, the man behind Batman's armors, gadgets and vehicles, believes that the rock is also what can be used to take out Batman -- and, by extension, Batwoman. But how can that be? Well, it's possible that the key to taking out Batwoman is actually Kryptonian technology.
Lucius is one of the most important members of the Bat-family. Bruce Wayne trusts him with his secret, and Lucius has also helped in his crusade by creating almost all of his arsenal. After all, Lucius is the one who designed the Batman armor, and now his son Luke is the one doing the same thing for Kate Kane. Luke remodeled the Bat-armor into something Kate could wear as the one and only Batwoman. Therefore, her suit still comes from something Lucius created, which means what can take out Batman is also what could eliminate Batwoman.
With those pieces of information, the likely answer is that the Batman/Batwoman armor is actually partially made of Kryptonian technology or armor. Perhaps such as a material is what helps keep the person under the cape and cowl safe from all manner of attacks, whether they come from guns, knives, or explosions. In the Arrowverse, the "Crisis on Infinite Earths" event created a new continuity, which means that it's possible Superman helped Batman in his crusade by giving him Kryptonian metal that could protect him -- either that or Bruce stole them without Clark's knowledge, something that is just as plausible given Batman's track record. Therefore, the Batman armor could have the same weakness as Superman himself. If that is the case, then Kryptonite would be the surefire way to get through the armor and properly kill the Caped Crusader.
Of course, there is also always the chance that Kryptonite could be used in a more overarching approach. It's possible that Lucius knew very well that Kryptonite is something that could come in-between Superman and Batman. Perhaps he understands that the only way to defeat Batman is by manipulating him into fighting Superman, the only one powerful enough to stop him for good. If that is the case, then Lucius might have just borrowed his plan from Batman v. Superman: Dawn of Justice's Lex Luthor. And if that comes to pass, Supergirl might be paying a visit to Gotham City very soon.
Created by Caroline Dries and developed by Berlanti Productions and Warner Bros. Television, Batwoman stars Ruby Rose, Rachel Skarsten, Meagan Tandy, Camrus Johnson, Dougray Scott, Elizabeth Anweis and Nicole Kang. The series airs Sundays at 8 p.m. ET/PT on The CW.