For Halo 3 do you have to beat the entire campain on Legendary to get the achievement?

Like, the entire campaign, starting with Solo Campaign (not countin co op) or can you just beat every level separately? I got about half way and got to the covenant, then started a new campaign to get the skulls, erasing the previous data. So would i have to re do it or just start on the covenant and beat the rest of the levels