Below is the complete list of Mobile Suits/Armors available in the game and how to unlock them. If you'd rather find out how to get them all by yourself, don't continue on. And if you see any mistakes, please notify me.

Mobile Suit Name	How To Get	Available In:
God Gundam	Start With	Street, Versus, Time Attacks, Survival
Gundam Maxter	Start With	Street, Versus, Time Attacks, Survival
Gundam Rose	Start With	Versus, Time Attacks, Survival
Dragon Gundam	Start With	Versus, Time Attacks, Survival
Bolt Gundam	Beat Street Mode with Gundam Maxter	Versus, Time Attacks, Survival
Master Gundam	Beat Street Mode with God Gundam and Gundam Maxter	Street, Versus, Time Attacks, Survival*
Devil Gundam	Beat Street Mode with all 8 Mobile Suits and then continuously fight the CPU in Versus**	Versus, Time Attacks, Survival
Gundam Wing Zero Custom	Start With	Street, Versus, Time Attacks, Survival
Gundam Altron	Start With	Versus, Time Attacks, Survival
Gundam Deathscythe Hell Custom	Start With	Street, Versus, Time Attacks, Survival
Gundam Sandrock Custom	Start With	Versus, Time Attacks, Survival
Gundam Heavyarms Custom	Beat Street Mode with Deathscythe Hell Custom	Versus, Time Attacks, Survival
Tallgeese III	Beat Street Mode with Deathscythe Hell Custom and Wing Zero Custom	Street, Versus, Time Attacks, Survival*
Gundam Epyon	Beat Street Mode with all 8 Mobile Suits	Versus, Time Attacks, Survival
Gundam RX-78	Start With	Street, Versus, Time Attacks, Survival
Zaku II	Start With	Versus, Time Attacks, Survival
Zaku II-S	Beat Street Mode with RX-78	Street, Versus, Time Attacks, Survival*
Hygogg	Beat Street Mode with Wing Zero Custom	Versus, Time Attacks, Survival
Acguy	Beat Street Mode with RX-78	Versus, Time Attacks, Survival
Ball	Beat Street Mode with RX-78	Versus, Time Attacks, Survival
Zeong	Beat Street Mode with Zaku II-S	Versus, Time Attacks, Survival
Big-Zam	Beat Street Mode with all 8 Mobile Suits and clear Time Attack A in 5 mins or less	Versus, Time Attacks, Survival
Nu Gundam	Start With	Versus, Time Attacks, Survival
Sazabi	Start With	Versus, Time Attacks, Survival
Quin Mantha	Beat Street Mode with Master Gundam	Versus, Time Attacks, Survival
Neue Ziel	Defeat 20 opponents in Survival Mode	Versus, Time Attacks, Survival
Gundam Physallis (GP-02A)	Beat Street Mode with God Gundam	Versus, Time Attacks, Survival
Full Armor ZZ Gundam	Beat Street Mode with Tallgeese III	Versus, Time Attacks, Survival
Hydra Gundam	Beat Street Mode with Tallgeese III	Versus, Time Attacks, Survival
Psyco Gundam	Beat Street Mode on Hard with all 8 Mobile Suits and Clear Time Attack B in 3 mins or less	Versus, Time Attacks, Survival

*-Once you earn it for Street Mode, beat Street with it to get it into the other modes.

**-Once you have fought enough versus battles to get it, after the fight ends, you'll be taken to the Progress Menu. I think it's 20 fights against 20 different Suits. I will try and get confirmation on this, though.