Successfully complete the indicated task to get an e-mail at the Terminal that 
will unlock the corresponding character in Mission mode:

Cecily Fairchild: Successfully complete Seabook Arno's Story mode missions.
Dozle Zabi: Accept the invitation to join Zeon, and successfully complete the 
assigned missions.
Four Murasame: Successfully complete Kamille Bidan's Story mode missions to 
unlock Four's friendship mission. Then, complete that mission.
Glemy Toto: Help Glemy establish his own faction while joining Axis to unlock 
another mission. Then, complete that mission.
Gym Ghingnham: Join Dianna Counter, and have normal or better relations with 
Gym to unlock another mission. Then, complete that mission.
Gyunei Guss: Play as Quess Paraya, and unlock Gyunei's friendship mission. 
Then, complete that mission.
Hayato Kobayashi: Have a good relationship with Hayato, and successfully 
complete his friendship mission.
Kai Shiden: Have a good relationship with Kai, and successfully complete his 
friendship mission.
Katejina Loos: Have a good relationship with Katejina, and successfully 
complete her friendship missions after obtaining a V2 Gundam license.
Lacus Clyne: Successfully complete Kira Yamato and Athrun Zala's Story mode 
missions to unlock a mission from Lacus in Kira's terminal. Then, complete 
that mission.
Lunamaria Hawke: Successfully complete Shinn Asuka's Story mode missions to 
unlock a mission from Lunamaria. Then, complete that mission after getting a 
Zaku II CA license.
M'Quve: Successfully complete the mission from Kycillia while joining Zeon.
Quess Paraya: Play as a non-Newtype. Increase your relationship with Quess 
until you get mail from her, then make the character a Newtype.
Ramba Ral: Have a good relationship with Ramba Ral until you get mail from 
Dozle while joining Zeon. Then, complete that mission.
Reccoa Londe: Play as Yazan Gable, and shoot down Reccoa.
Rosamia Badam: Have the best relationship with Kamille after joining AEUG to 
unlock another mission. Then, complete that mission.
Sarah Zabiarov: Have a good relationship with Sarah and Scirocco and a bad 
relationship with Reccoa to unlock a mission from Sarah. Then, complete that 
mission.
Sleggar Law: Play as a female character, and have a good relationship with 
Sleggar to unlock his friendship mission. Then, complete that mission.
Yazan Gable: Have a good relationship with Yazan after joining Titans to 
unlock a test mission. Then, complete that mission.