Successfully complete the indicated task to unlock the corresponding MS licenses 
in Mission mode:

Char's Z'Gok: Have a good relationship with Char, and successfully complete 
his second license mission.
Char's Zaku: Have a good relationship with Char, and successfully complete his 
first license mission.
Destiny Gundam: Successfully complete Shinn's Story mode missions, and have a 
good relationship with him. Then, complete his license mission.
God Gundam: Have a good relationship with Domon, and successfully complete his 
license mission.
Gundam: Have a good relationship with Amuro, and successfully complete both 
his license missions.
Gundam Epyon: Have a good relationship with Milliardo, and successfully 
complete his license mission.
Gundam F91: Successfully complete Seabook's Story mode missions, and have a 
good relationship with him. Then, complete his license mission.
Gundam MK-II AUEG and Titans: Have a good relationship with Kamille, and 
successfully complete both his license missions.
Gundam Wing Zero: Have a good relationship with Heero, and successfully 
complete his license mission.
Hyaku Shiki: Have a good relationship with Char, and successfully complete 
both his license missions.
Infinite Justice Gundam: Successfully complete his Story mode mission, and 
have good relationship with him. Then, complete his license mission.
Master Gundam: Get God Gundam's license. Have a good relationship with Touhou 
Fuhai, and successfully complete his license mission.
Musha Gundam: Defeat 5,000 troops, and successfully complete the corresponding 
Free mission. Then, complete Free missions 1 through 6.
Musha Gundam MK-II: Successfully complete 50 missions, then successfully 
complete the corresponding Free mission. Complete Free mission 7, then 
complete his license mission.
Nu Gundam: Unlock all UC licenses, and have very good relationship with Amuro. 
Then, complete his license mission.
Quebeley (Haman): Have a good relationship with Haman, and successfully 
complete her license mission.
Quebeley (Puru/Puru Two): Have a good relationship with Puru and Puru Two, and 
successfully complete their license mission.
Sazabi: Have Char's Zaku, Char's Z'Gok, and Hyaku Shiki's licenses. Have a 
very good relationship with Char, and successfully complete both his license 
missions.
Strike Freedom Gundam: Successfully complete Kira's Story mode missions, and 
have good relationship with him. Then, complete his license mission.
The O: Have a good relationship with Scirocco, and successfully complete his 
license mission.
Turn A Gundam: Have a good relationship with Loran, and successfully complete 
his license mission.
V2 Gundam: Successfully complete Usso's Story mode missions, and have good 
relationship with him. Then, complete his license mission.
Z Gundam: Have a good relationship with Kamille, and successfully complete 
both his license missions.
ZZ Gundam: Have a good relationship with Judau and Roux, and successfully 
complete both their license missions.