Beat the game on Easy to unlock 'Unbreakable Melee Weapons' and 'Bullet Reflection' options. Beat the game on normal to unlock 'Vampiric Health' and 'All weapons', and beat it on The One difficulty to unlock the 'Infinite Health' option.
The One mode:
Beat the first level 'Lobby Dreams' without dying in order to unlock The One difficulty. As you may imagine, it's the hardest setting.
Zion Archive level:
Upgrade the icon in the 8 o'clock position during the 'Atman Principle' to unlock the Zion Archive at the level selection screen.
Bonuses: Follow the directions to get the breifcases containing various bonuses:
Machine Gun Kick combo:
During 'The Chase: I need an Exit', the briefcase is found in the corner of the market area behind some fruit stands.
Quick Kicks combo:
During 'Storming the Drain', touch the top two platforms in the second to last room.
The Beginning Of The End combo:
During 'Seraph's Apology', return to the teahouse from the theater and destroy one of the tables as well as all eight support columns.
The Codebreaker combo:
During 'Weapon Training', the briefcase is in the Operator's secret stash in the upstairs corridor when returning to teahouse.
The One combo:
During 'The Burly Brawl', defeat 30 Agent Smiths and the briefcase will appear in the center of the level.
Ultimate Hyper Strike combo:
During 'Redpill Rescue: The Security Guard', defeat the SWAT team on the stairs within the time limit.
Storyboard Sequence 1:
During 'Red Pill: The Key', complete the bonus objective in the second room by not using any guns.
Storyboard Sequence 2:
During 'The Frenchman', kill the first set of enemies, go to the red cross in the dungeon and go right to find the briefcase.
Thanks to Revolution reader Komodan, O-su!, and billigher!