I honestly don't know why Cordia would feel guilt. I can certainly see remorse, for the loss of a lover and a close friend.
But there's also betrayal in there.
Cordia's guilt is mentioned few times throughout the game; once by Wilfred in the "Portend" event, second time while not explicitly the word "guilt" is used, it's very much implied in that with words such as "fault" or "responsibility" in Cordia's Office recording; Recording 7 iirc).
I can think of couple of people Cordia would feel guilt for:
1) Rina & her son, the MC
Rina was the first real friend Cordia made, and things happened which drove them apart and a war was waged on between them where they ended up being enemies (Giocabbe's whole "Sorry I couldn't help when the other Serpents betrayed you" line he says to Cordia in their meet to plead mercy for Straffan).
This in my eyes drove Rina to the point where she seemed to be willing to take her own life, as well as her own son.
Not to mention due to the whole war between Cordia and Rina, MC didn't get a proper childhood (I'd imagine Kaskars did their best, but still..... I think child MC would have had it a bit rough until he got to meet with Jalen).
2) Luna & Lucan
Due to the events in "My name is Luna", Luna went through a traumatic experience that scarred her for life, and Lucan lost his life.
Hearing from Luna that she was forced to shoot Lucan I'd imagine bears a tremendous weight on Cordia with extreme guilt (probably as to how she feels, as the Donna failed to protect her own family).