To unlock hidden mechas in the game, you have to clear Arcade mode at least once to unlock one hidden mechas for your next game. Below here would be the list to unlock all available mechas, with the requirements.

Unlockable	How to Unlock
MS-18E Kampfer	Clear Arcade Mode twice
RX-77_Guncannon	Clear Arcade Mode once.
RX-78GP01 Gundam "Zephyranthes" / RX-78GP01-Fb Gundam "Zephyranthes Full-Vernian" [MSG-0083]	Clear Arcade Mode three times.
ZGMF-X42S Destiny	Clear Arcade Mode four times.