On stage 24, defeat Takuma with Sousuke. On stage 29, defeat Zaied with Sousuke. On sage 30, defeat Gauron with Sousuke. You should get him on stage 34.
Fourth Original Mecha
Beat the game with the Bellezelute, Coustwell and Granteed.
Gai Daigouji
Take the Nadesico Route on stage 21. He will join during stage 44 on the Nadesico Route.
Great Zeorymer
Do not use Zeorymer unless the game forces you to. Go with the Nadesico on stage 11 and let Zeorymer destroy Lanster of Wind. On stage 21 go with the Archangel and let Zeorymer destroy Briest of Fire and Gallowin of Water. On stage 29 let Zeorymer destroy Rose C\\\'est La Vie of Moon. On stage 32, let Zeorymer destroy Dinoderos of Earth, Burrstone of Mountain and Omzack of Lightning. Afterwards, Great Zeorymer will come. Destroy it with Zeorymer. You should get Great Zeorymer on stage 36. After this point, you may use Great Zeorymer whenever you want.
IWSP Pack
Go with the Archangel on stage 11 and 37.
Nobel Gundam
Do not destroy the Nobel Gundam on stage 38 and then convince Allenby with Rain on stage 41. Afterwards, destroy the Nobel Gundam.
Tekkaman Rapier
Have Tekkaman Blade defeat Tekkaman Evil on stage 34 and Tekkaman Axe on stage 36.
Bonta-Kun...