Access Simulator mission 6
All characters unlocked.
Beam Rifle
complete all of 2nd run through and complete all simulations with an S rank while using the Dom Tropen
Char Aznable, the Red Comet, and his MS-06S Zaku II
Beat game. Play through simulator mission one - Practice - with an S rank (though admittedly, I was able to get him with an A rank).
Gaia of the Black Tri-Stars and his MS-09 Dom
Beat game. Complete mission 12 on the second time through the game - this unlocks the simulator mission where the Black Tri-Stars make their attack on the Trojan Horse.
Garma Zabi, and his custom MS-06Fs Zaku II
Beat game. You need to complete simulator mission 2 - Breakthrough - with an A or S rank. (Honestly I'm not sure about the A rank, though again, it happened with me. So try for an S regardless)
Get The Gouf Form Of Zaku
Get up to Mission 6 in story mode. Then select Lt. Lou Roher and it shall have Gouf MP.
Hayato's guncannon
Get 50 kills with his guntank.
Hidden Character - Char Aznable
Get an S Rank (8,000+ points) in Simulation Program 1 after finishing the game once.
Hidden Character - Garma Zabi
Get an S Rank (8,000+ points) in Simulation Program 2.
Kai in his Guncannon, Hayato in the Guntank, and Lt. Agar in his Guncannon
Beat game. Complete the 'Attack Jaburo' mission on the second run through the game.
Kai's guntank
Get 50 kills with his guncannon.
LC Garret Schmitzer
You can get his customized MS-05S Zaku I by just beating the game once.
Mudrock full specs
Unlock mudrock gundam. Then get an S rank on a federation sim. After the stage Agar will have full Mudrock Gundam.
Ramba Ral, and his nifty blue YMS-07B Gouf
Beat game. Open up the simulator mission about his attack on the Trojan Horse, which is achieved by beating mission 8 the second time through the game. Note, not -simulator- mission 8, in-game mission 8. Once you've beaten it, Ramba Ral is yours.
RX-78-6 Mudrock gundam
Beat game. Completing Simulator missions 27-31 with A or S ranks.
Sayla Mass in the RX-78-2 Gundam, and Amuro in the same machine
Beat game. Complete the missions.