I've noticed that no one has asked for this. There are six [AMAZING] tracks in the demo that recently came out with Advent Children Complete. Obviously they have no titles yet, but they are, in order of appearance (I'm pretty sure):

1. battle theme remix/rearrangement (also found on the official site)

2. boss theme (the crazy piano/orchestral song heard when fighting the mechanical scorpion atop the train, the FFXII-Judge-looking knight on that collapsible bridge thing, and the [mechanical?] Behemoth on the highway)

3. battle theme (the regular - and, in my humble opinion, better - version first heard in round two of the scorpion fight, and then in all the regular encounters after that)

4. highway background theme 1 (heard only in the Lightning/Sazh part of the demo as they traverse the highway)

5. foreboding cutscene song (first heard when Lightning and Sazh come across a PSI-COM soldier who summons the red and white beasts, and in most other cutscenes after that)

6. highway background theme 2 (heard only in the Snow/Team Nora part of the demo as they traverse the highway; the only bad song of the six, in my opinion - and that's a good sign)

There might be one or two more songs, but I think I've typed them all here. If anyone who happened to get the special edition ACC and is playing the demo is interested in uploading these tracks, I'd greatly appreciate it. I'll try not to get my hopes up, though, seeing as how (I'm guessing) not many people, if anyone, here bought it. Thanks in advance!

EDIT: You can get a feel for some of the tracks I'm looking for in these IGN videos:
http://ps3.ign.com/dor/objects/826843/final-fantasy-xiii/videos/ff132.html
http://ps3.ign.com/dor/objects/826843/final-fantasy-xiii/videos/ff133.html
http://ps3.ign.com/dor/objects/826843/final-fantasy-xiii/videos/ffxiii_snow_1.html

But if you want to see the full demo and hear all the songs, I suggest you check out the live vlog below and watch this guy play through it. He also shows the new Agito and Versus trailers that came with the demo. Seems he doesn't come online until evening (it's currently 3:30 p.m. Pacific time where I am, and he ain't on yet), so check back regularly.
http://www.justin.tv/esegk

A more reliable version of it can be found on YouTube in HD quality (a playlist tab appears at the top-right of every screen if you want to see the other parts).
http://www.youtube.com/watch?v=qMzMZUL8okg

3. battle theme (the regular - and, in my humble opinion, better - version first heard in round two of the scorpion fight

I agree. This is the theme we heard in the very first trailers of this game and I've come to love it a lot. Fortunately, it should be possible to rip the track from the demo. Unfortunately, making iso's of ps3 games/demo's much less extracting the content from them does not seem like a common thing from what I've seen. So it may be a while before we can get some direct rips of these tracks. I pray I'm proven wrong though.

*edit*
This was all I was able to find for now:
http://www.sendspace.com/file/zbk3sx

here they are in higher quality:
http://www.sendspace.com/file/6i3vzx

Wow, great! This will most certainly do for now. Thanks!

you're welcome.

hey everyone, i managed to grab the battle theme with higher quality than the previous ones and made a nice loop out of it.
here (http://rapidshare.com/files/222808650/FF13_-_Battle_Theme.mp3)

Holy crap, sir; you-are-AMAZING!

back with more =D
Boss battle with a nice loop to it (http://rapidshare.com/files/223191188/FF13_-_Boss_Battle.mp3)

Many thanks, friend! You've really been making my day(s). Now, if only you could rip the Hanged Edge highway song (complete with crazy violin solo)... :p

5. foreboding cutscene song (first heard when Lightning and Sazh come across a PSI-COM soldier who summons the red and white beasts, and in most other cutscenes after that)

6. highway background theme 2 (heard only in the Snow/Team Nora part of the demo as they traverse the highway; the only bad song of the six, in my opinion - and that's a good sign)

These are the same songs, If I'm right, it begins with the foreboding part and then goes into the more militaristic part.

Oh, didn't know that. I'll take your word for it :)

These are the same songs, If I'm right, it begins with the foreboding part and then goes into the more militaristic part.

Nope, sorry but they're different. The piano in the opening of the cutscene does play the same notes as the chimes in the beginning of Snow's field music, but they're pretty different from that point on. Snow's field music is much better, in my opinion.

The Tacit One, if you're still looking for the cutscene music, I've ripped it along with the rest of the music in the demo (no sound effects or background ambience). Here's a link (http://www.sendspace.com/file/i2a8k7), if you're interested.

This is a lot better than what i got last time

Wow, absolutely amazing Lian_Kazairl! Thanks so much.