After doing these prerequisites, don't forget to read the new mail in the Terminal to unlock the characters.

Character	How to unlock
Cecily Fairchild	Finish Seabook Arno's story missions
Dozle Zabi	Accept invitation to join Zeon and clear the missions given
Four Murasame	Finish Kamille Bidan's story missions and read the new mail to unlock Four's friendship mission; clear it
Glemy Toto	Agree to help Glemy establish his own faction while joining Axis, and clear the mission given
Gym Ghingnham	After joining Dianna Counter, have at least normal relations with Gym and he will send a mail; read and clear the mission given
Gyunei Guss	Play as Quess Paraya, and read Gyunei's mail to unlock his friendship mission; clear it
Hayato Kobayashi	Have good relations with Hayato and clear his friendship mission
Kai Shiden	Have good relations with Kai and then clear his friendship mission
Katejina Loos	Have good relations with Katejina and read her mail to unlock her friendship missions; V2 Gundam license is required to clear them
Lacus Clyne	Clear Kira Yamato & Athrun Zala's story missions, and read Lacus' mail in Kira's terminall; clear the mission given
Lunamaria Hawke	Clear Shinn Asuka's story mission and read Lunamaria's mail; Zaku II CA license is required to clear the mission
M'Quve	Read a request mail from Kycillia while joining Zeon and clear the mission given
Quess Paraya	Play as a non-Newtype, build up relation with Quess until you receive mail from her, then make the character a Newtype
Ramba Ral	Read a request mail from Dozle while joining Zeon and clear the mission given; also need to befriend Ramba Ral first
Reccoa Londe	Play as Yazan Gable and shoot down Reccoa in any mission
Rosamia Badam	Have best relations with Kamille after joining AEUG, then read his mail and clear the mission given
Sarah Zabiarov	Have good relations with Sarah and Scirocco, bad relations with Reccoa, then read Sarah's mail and clear the mission given
Sleggar Law	Play as a female character, have good relations with Sleggar, and then read his mail to unlock his friendship mission; clear it
Yazan Gable	Have good relations with Yazan after joining Titans, read his mail and clear the test mission given