Here is a list of all the songs you can unlock in Sudden Death mode just by passing them once.

(K-POP) Forever Love by Fin.K.L

(K-POP) Love Song: Steve Yoo

(K-POP) Valenti: BoA

(POP) Kiss Me: Debbie Scott

(POP) Power of Dream: Victoria

A great way to unlock most of the PIU songs would be to play the NEW songs when you can, because they WILL unlock in another mode eventually if you don't have certain conditions for them.