Edit 2: Nickelodeon removed the individual files from dropbox (probably due to some unexpected traffic =P), but the nusic tracks can still be downloaded at the mediafire link below.
Edit: Some people on the ASN forums are reporting trouble with the links. If the above don’t work use this, someone zipped the files and uploaded them to mediafire: http://www.mediafire.com/?3vai0dea3fzvlkl
-Amon in the Shadows (This one is very much like A:TLA music, and it’s creepy, as the title implies)
-Bolin Wants to Know (Again, very A:TLA type music, and it’s beautiful, there are stringed instruments)
-Hardboiled…Afraid (Sad, somewhat similar to A:TLA music but has a slightly different feel)
-Hittin’ On All Sixes (Completely different from A:TLA—very jazzy and upbeat)
-Legend of Korra main theme (Has a traditional Avatar feel, but uses different instruments and is unique)
-Lost My Heart in Republic City (More roaring 20’s jazz style, only with Asian instruments. This one is actually adorable).
-The Rally (Definitely the most intense song of the bunch; very dark. Contains both old A:TLA elements and new ones)