Rock Climbing Stage skip
Start a game and enter the item selection screen. Then, press Triangle, Square, Triangle, Square.
Level skip
Start a game and enter the item selection screen. Then, press L1, L2, R1, L1(3), R1(2).
View ending sequence
At the title screen, press R1, L1, R1, L1, R1, L1.
The image featured at the top of this post is ©The Legend of Heroes: Trails of Cold Steel III key art.