or maybe he is yelling for the republic because the achievement is for helping the New California Republic
thats the most logical explanation
Yep, undoubtedly a reference to the Clone cheering the victory of the New California Republic.
No kidding, huh? I never would have guessed. Look, the fact that it's referring to the NCR is obvious, but Achievements often have puns and double meanings.
For example, the companion achievement, "Render Unto Caesar" obviously refers to Caesar's Legion, but it's also a biblical reference to the passage Matthew 22:21- "Render unto Caesar what is Caesar's, and unto God What is God's."
I'd consider those two missions to be the turning points in the game. I'm willing to bet that those are the missions where the game forces you to choose a side, and at the very least makes it very difficult to have good or neutral relations with the other side at that time.
If one of the achievement names is a reference to the Bible, why couldn't the other one reference Star Wars, which is arguably of equal cultural importance to some people, especially considering that "Jedi" is an officially recognized religion in some countries?