Complete the missions on the Zeon faction:

Effect	How to unlock
Gelgogg Cannon	Use MS-14A and Zaku Cannon for 5 missions each
MS-05 [3S]	Use the MS-05 for 5 missions
MS-05[RR]	Use MS-07B for 5 missions
MS-06R1A	Use MS-05[3S] for 5 missions
MS-14S	Use MS-14A for 5 missions
Perfect Zeong	Use Zeong for 5 missions