Time attack mode
After finishing the first two objectives on all levels in every scenario you will unlock the first ending sequence. Then, press Square at the scenario selection screen.
Mission Objectives 2
If you want to unlock Mission Objectives 2 for every character and/or scenario, finish 19 stages in any order. Then, press L1 + R1 while the stage is highlighted at the scenario selection screen. REMEMBER: You will automatically obtain it after completing the random 19 stages.
Brain Cell Revival (Zuno) puzzle mini-game
By finding Archive 087 in Kyoya Sudo's stage (03:00 on Day 3).
Hidden FMV sequence
After finishing the game and finding all 100 Archives. A bonus FMV sequence will be unlocked at the top right corner of the scenario selection screen.