This will unlock naturally playing through mission mode, but you must view the Terminal faction messages for the following characters as they do not appear in missions:
Relena, Diana, Bask, Gihren, and Rain
update: more details
Relena Darlian - Can only meet her if you join Operation Meteor
Torres - Will sometimes appear in a friendly or enemy ship. Just get to the briefing screen of the Friendship Mission, "Good Luck, Loser!" and check the Unit/Field Info. This mission always has a friendly ship. Check the field to see if Torres is onboard the ship as an ally. If he isn't, back out and reload the mission to the briefing screen again and check it again. Repeat until he appears and beat the mission to gain his Friendship.
Leina - Sometimes appears in a ship, but you can easily meet her by joining A.E.U.G. (ZZ Gundam) and then joining and clearing all the missions for Judau's Junk Dealers faction.
Dianna Sorrel - The only way to meet her is by joining the Moonrace faction