Successfully complete Bionic Commando Rearmed to get a codes for "Purple Matrix", "Retro costume", and "Prototype weapon" that can be entered in Bionic Commando. Note: The codes are different between Xbox 360 consoles.

Retro Outfit: The code is already unlocked in the Database in Bionic Commando: Rearmed.
Prototype Weapon: In Bionic Commando: Rearmed, find the floating FSA icon in Area A. It is located behind an electrical barrier you must backtrack to after removing. This will unlock the code in the Database.
Purple Matrix: In Bionic Commando: Rearmed, go to Area 0 and look for the open Yashichi door after collecting all twelve Yashichis. Collect the "Purple Matrix" inside. This will unlock the code in the Database.