Halo 3 Armor Permutations

Body Pieces
Spartan
EVA.................Complete Tsavo Highway on Normal, Heroic, or Legendary
EOD.................Complete Tsavo Highway on Legendary
Scout...............Unlock "Too Close to the Sun" Achievement (Destroy an enemy banshee with the Sp'laser or missile pod in a ranked playlist or campaign)
Elite
Flight...............Complete Tsavo Highway on Heroic or Legendary
Ascetic............Unlock "Up Close and Personal" Achievement (Kill 5 enemies via melee or assassination in a ranked FFA playlist)
Commando....Unlock "Triple Kill" Achievement (Get one triple kill)

Shoulder Pieces
Spartan
EVA.................Complete The Ark on Normal, Heroic, or Legendary
EOD................Complete The Ark on Legendary
Security..........Earn 750 Gamerscore Points
Scout...............Unlock "We're in for some Chop" Achievement (Destroy an enemy vehicle with a piece of equipment in a ranked playlist or campaign)
Elite
Flight...............Complete The Ark on Heroic or Legendary
Ascetic............Unlock "Overkill" Achievement (Get one overkill)
Commando....Unlock "Killing Frenzy" Achievement (Get one killing frenzy)

Head Pieces
Spartan
EVA.................Complete Campaign on Normal, Heroic, or Legendary
EOD.................Complete Campaign on Legendary
Security...........Earn 1,000 Gamerscore Points
Scout................Unlock "Used Car Salesman" Achievement (Destroy an enemy vehicle containing 3 enemies in Campaign or ranked playlists)
Mark V.............Unlock "UNSC Spartan" Achievement (Reach Sergeant ranking online)
ODST...............Unlock "Spartan Graduate" Achievement (Earn 5 EXP or complete 10 ranked matches)
Rogue.............Unlock "Spartan Officer" Achievement (Advance to the Spartan Officer ranks online)
Elite
Flight...............Complete Campaign on Heroic or Legendary
Ascetic.............Unlock "Steppin' Razor" Achievement (Get one triple kill with an energy sword in ranked FFA)
Commando....Unlock "Overkill" Achievement (Get one overkill)

At this time, the Hayabusa (Samurai) is unknown what is needed to obtain it. I'll keep you posted.

Edit: Here's a good picture of armor permutations (Courtesy of Dolemiteb for making it HaloIsMegaKewl for posting it): http://i15.photobucket.com/albums/a371/SweetTooth_/armors.jpg

Special thanks to WhiffleBallTony from the B.net forums for providng this information