Supreme Logician - I started out deciding that I had to pick an Advance Wars theme. They're all so colourful and say so much about their character. Days of Ruin gets a bad reputation of being purely "loud guitar" for each character but I always felt Lin's always stood out. It gives a true sense of a tactical commander and plays it quite well. The other piece that came to mind for Days of Ruin was
We Will Prevail, but it would require explaining that the game is a dark world with this character trying to push forward hope.
Unshakable Faith - I'm not sure this one needs an introduction. It sets the stage for the final battle and gives the sentiment that it's do or die...and there's no dying. Well, except to the Berserk staff that you forgot existed.
The Battle for Everyone's Soul - I was questioning myself on this choice. Part of my love would require describing another Persona piece. But the love of piano and its electric guitar mix won out. It's an uptempo piece which sets the stage well for a final battle against what's effectively a god.
(The part which really gets me is the change at 1:45. It basically plays Aria of the Soul, the theme for another key part of the game)
Blooming Villain - The biggest reason is the guitar. The rhythm change is so perfect in a boss battle. The rest of it gives a fairly generic feel against a corrupted lord...but the change in pace always gets me. Another piece which works similarly is The Genesis (Persona 4), where is mostly a slow and overbearing piece. Then breaks into an orchestral version of the familiar and uplifting battle theme you're used to for a brief period of time (5:45 if you're looking for it), lending itself greatly to the general uplifting nature of Persona 4.
Life Will Change - Everyone talks about Rivers in the Desert (which really is a great piece and used as the "climactic boss" theme). I think this one fits the whole acid jazz style the game puts forth. It doesn't hurt that the piece is ultimately extremely uplifting at the same time. I think it's a better piece in a vacuum though you could easily make a case that Rivers in the Desert makes a better contextual piece.
The Person is Then Called Away From War - Persona Q has one of the best OSTs I can remember. This one stands out as it was done by Yuzo Koshiro (Etrian Odyssey is probably his biggest claim to fame) and has all his hallmarks, including the mix of symphonic orchestra and electric guitar. I picked the impossible name over any other piece because it's really interesting to hear an Etrian Odyssey piece in a Persona game. If it weren't done in a vacuum and I could explain each piece, I might have gone with Changing Me or Laser Beam instead. Really, I recommend listening to the whole OST for the game. It's a shame it got attached to a mediocre game.
Vs Champion Lance, Red - Not really many reasons I need to explain this one I think. It's probably the best Pokemon battle theme I could find. It's a bit of a nostalgia pick as the battle against Red in Gold and Silver is one of the fondest memories I have of Pokemon and an excellent piece for measuring a sequel.
Dark Prison - Super Robot Wars has a massive collection of excellent music pieces. Villain Mary Sue Shu Shirakawa has one of the best, representing the fact that he's more or less an oppressive force of nature than a human. I was always tempted to pick other pieces but they also required descriptions. Shooting Star H is a brilliant piece as well but requires describing the character it portrays. Same goes with The Sword that Smites Evil.
The End of a Thought - Not much that can be said about it that hasn't been mentioned before. It's a climactic piece which juxtaposes the sheer chaos in the opening to the quiet moments. Probably would have gone to Romance of the Three Kingdoms had I not picked Tales.
Blue Bird Lamentation - Oh boy was I worried about picking this one. It's set one of the most heartbreaking moments in Virtue's Last Reward and really sets the stage for Laura Bailey's amazing performance in the scene. It's wonderful in its own right but it really doesn't do it justice to hear it on its own. The other piece I could have gone with is Morphogenetic Sorrow...the only piece I've ever heard and then begun apologizing to the in-game character after.