Irony of Clancy's plan to destroy the research about the cure
Clancy Grey, President Grey's son, tricked Ruby and others to go back to California just so he could destroy his mother's research about the cure for IAAN. He tried to burn the documents but Ruby got to them before they were destroyed. In the final chapter he is bragging about destroying the research and Ruby shows them that he failed. If Clancy hadn't made Ruby and others go to California and the Children's League building then the evidence would have surely been destroyed. But this way, ironically, he only contributed in saving the documents.
Irony of Jude's death
Jude's death is ironic because he believed in the change, believed that the Children's League could go back to be what it was originally created for. Just when things appeared to go in that direction, Jude was gone together with the Children's League organization.
Irony of Children's League
The Children's League wasn't always the corrupted organization that only used the PSI kids as weapons. Its creator Alban had all the right intentions when it first started and when Cate first joined. He eventually gathered the wrong people around him which made the Children's League corrupted. After Alban's death the fall of the Children's League soon follows.
Ruby's irony
Ruby has an ironic view and her narration is filled with ironic undertones, for instance when she talks about the corrupted agents "whispering plans and sweet nothings" into Alban's ear and how they made Alban focus on the "big picture" while they controlled everything in the Children's League.