These are only that which I have personally seen unlocked, there are many more rumored, but I have yet to confirm them.

*For most of these you'll need to have beaten the mission mode at least once.

Unlocking EFF Shield(like that of Gundam and GM's)-After completing the game, successfuly complete practice mission 1 with Austin's Zaku I

Unlocking Lt. Commander Garret Schmitzer with his MS-05S Zaku I custom-Simply Complete the mission mode once

Unlocking Char Aznable and his MS-06S "Red Comet" Zaku II Custom-On simulator mission I "Practice" receive an A or an S ranking

For Garma Zabi and his MS-06Fs custom-Receive an A or an S in simulator 2-Practice II

For Ranba Ral and his YMS-07b Gouf-Complete the entire mission mode a second time up through at least mission 8

For Gaea of the black Tri-Stars and his MS-09 Dom-Complete up throug mission 12 a second time

For Agar in his guncannon completecomplete mission 10"Attack jaburo" a second time
In addition, complete simulations27 through 31 with an A or S to receive Agar;s RX-78-4 Gundam madrock

For Sayla Mass in the RX-78-2 gundam, receive a C or less in three seperate EFF simulation missions

For Amuro Rei, in the RX-78-2 receive an S in all EFF missions

I know Kai and hayato are selectable, but am unaware of precisely how to achieve them, if all of the afformentioned is completed, you should receive tham as well.