The EOD Armor set in Halo 3 is a bit more difficult to get than armor such as the EVA set. Rather than beating campaign missions on Normal, or Heroic, you will need to beat them on the Legendary difficulty.
To unlock the EOD “Body”, beat “Tsavo Highway” on Legendary.
To unlock the EOD “Shoulders”, beat “The Ark” on Legendary.
To unlock the EOD “Helmet”, beat the Campaign on Legendary.
