One of our most dedicated members, Mystic, has written an amazing guide on getting the signature takedowns on Burnout Legends for the PSP.
You can view it by clicking Signature takedowns on the left menu, or by clicking the link at the end of this post.

Mystic has also posted the track list for Legends which you can view by clicking the link at the end of this post.

Links:
Burnout Legends Signature Takedown Guide
Burnout Legends Track List
Register at Operation Burnout