Zero's Black Armor: Have all of Zeros metals, and then beat the game.
Zero's Sigma-Blade: After beating the game, use the cleared save and you can get the Sigma-Blade at the lab.
Axl's White Armor: Beat the final boss with a double attack using Axl. You must have all of Axl's metals,
X's Ultimate Armor: Beat the game with all of X's metals and all eight pieces of armor.