When you're in arcade mode level 100 and/or higher, Ex characters will begin to challenge you. Beat them all to open them.

When you're in arcade mode level 199, beat Leopaldon to open him.

When you're in GG Boost mode, beat Kakusei Sol and Ky in the final stage to open them both.

Play Scramble in RK II Factory, but it has to be on normal difficulty. Complete the final stage with total score of 1,500,000 or more. Robo Ky II Substance will want to fight you. Beat him to get Kakusei Sol and Kakusei Ky as playable characters.