tl;dr brainspam

(Random Tech) "Shields at 80%... 70%-- holding at 70%! Reflective layer dissolving!"
(Kain) "Total damage update?"
(RT) "Minimal, but the Trevelyan Type 40 Engine is damaged."
(Kain) "Oh, we'll pay them back for that a hundred fold..."
(Alexander) "That armada... it's huge. All this for us?"
(Gale) "... All of the stars in the heavens are our enemies...?"
[deskslam]
(Helena) "Ha! They're not worthy of being our enemies! So what if the entire world is against you. I'll smash them. Along with space-time itself, if I have to!"
(Alexander) "... Ready the Wave Drive Cannon! Target the central weakness of the CAS Octava!"

...
So basically Alexander's one in-character dream that I've written is some sort of Gurren Lagann-Romance (based solely on the characters involved, I'll grant) hybrid.
(More than his actual life is, I mean.)
I think he just justified his existence, personally.