Kill both Manipulators. They are so easy we don’t even need to detail a strategy for you. It is not over yet.
Boss Fight: Proto FalCie Adam (Round 2)
This version of Fal’Cie focuses on physical damage output, so Bravery and Protect on all opponents, while you need to take down bigger chunk of HPs. Smite off both Manipulators to cause the main body’s attacks to become weaker. Fal’Cie will eventually recall both Manipulators at full HPs, but they fall easily.
Defeated a powerful enemy with valiant skill.
A perfect Cinematic Action awards you the Crystal Apple . Hello, Live Trigger: (The Proto fal’Cie keeps regenerating. What’s the battle strategy?) - there’s one more version of Adam to defeat, so press Circle to fight it.
Proto FalCie Adam (Round 3)
This version of Fal’Cie focuses magic damage, hence you will immediately be pestered with Imperil and Curse on all party members, so cure that with Esunas. Meanwhile all opponents gain Faith status. Smite off both Manipulators to cause the main body’s magic attacks be reduced to simple lv1 element spells. Fal’Cie will eventually recall both Manipulators at full HPs, but they fall easily.
When you win that battle as well, there will be the same Live Trigger: (The Proto fal’Cie keeps regenerating. What’s the battle strategy?) - press Square to advance the game.
Nab the AF200 AUGUSTA TOWER FRAGMENT - Proto fal’Cie Adam Fragment (01/04) + 6000CP ! A Live Trigger Cube has also appeared nearby, so claim its contents. With the boss done and dusted, check the terminal to free up the access to the shiny gate nearby. Use the Artefact of Rebirth on the shiny gate to unlock the AF4XX Academia timeline.