Seablade Mission select
Pause the game and press X, Y, L, X, R(2). Exit to the mission selection screen and all of them will be unlocked.
Invincibility
Pause the game and press R, Y, L, X(2), R. Although your health will still decrease, you will not lose a life when it reaches zero.
The image featured at the top of this post is ©The Legend of Heroes: Trails of Cold Steel III key art / Original