"Laser Beam" the boss battle theme, is a fast-paced, intense piece that will get you pumped to face off against the labyrinth guardians.
The F.O.E Battle Theme gets you pumped up whether you're actually fighting them or just running the hell away. It's also used for Elizabeth's Bonus Boss battles.
"The Person Is Then Called Away From War" is used for the final bonus battle against Zeus!Elizabeth, which is only available by completing all of the extra requests on a New Game Plus. It has a very Etrian Odyssey feel, which is helped by the fact that the very composer of said game created this piece.
"Proof" is a heartbreaking yet beautiful theme once the truth behind Rei is revealed, while also showing the intensity of her unwillingness to accept it.
Footsteps of Time, which plays throughout the game's final stretch, is a bit of a departure from Persona's usual style of music, employing elements such as choir, pipe organs, and a part of the percussion which sounds like a ticking clock. Starting out quiet, becoming bombastic, and then going into a section which sounds rather contemplative, it can be seen as a musical metaphor for the passage of time. There's also a very small segment which sounds suspiciously similar to Castlevania's "Bloody Tears".
On a more low-key note, Labyrinth Culture Festival is a relaxing but bouncy theme that plays over Strolls, where your companions take the time to relax a little and learn more about each other. It captures the mood perfectly.