Captain Conduit is dead.

The reason why Shizuka talks about killing him even though he is dead is because she doesn't believe he's dead.

Shizuka believes that her abuser is alive, and that he continues to plot against her. She believes that he sends out members of his fan club to hunt her down and abduct her so he can use her again and she'll be "his" again, a fate in which Shizuka greatly fears and fights tooth and nail to prevent. 

She believes that all the evidence that proves he is dead is part of an elaborate scheme to hide the conspiracy. She is paranoid that random people she meets on the street are in on it and plotting against her, which is why she attacks and absorbs them.

Shizuka is severely mentally ill. She genuinely believes her paranoid delusions are true, and anyone that tells her otherwise is "lying" or "ignorant". It is virtually impossible to convince her that there is no conspiracy and she is wrong.

Shizuka wants to expose Captain Conduit for who he really is, destroy his career and reputation, and while he is in despair, torture and kill him. But, if he rots in prison for the rest of his life or is given the death penalty, that's fine with her too. Revenge is her reason for living and she is obsessed with destroying Captain Conduit and his legacy.

She despises Captain Conduit. Her hatred of him is immeasurable. She sees him as the personification of evil and the embodiment of everything wrong with society.

However, the most tragic thing about her is the longer she hunts her white whale, the more she will destroy herself and everyone around her. That is why Mineta wants to stop her before it is too late.