To get the time machine described in Dynal, Duna and Raptin and in The 3 guh robots talk to Dr.Diggins in the teleporter room and help him.

Vivosaur	How to unlock
Dynal, Duna and Raptin	After you get the time machine, defeat him in his starship.
Dinomaton, Duna and Raptin	Revive the first 100 Vivosaurs.
Frigi	Defeat the 3 main BB bandits after you beat the game.
Igno	Beat Saurhead a certain amount of times after you beat the game.
Squik and his other elements	Get all vivosaurs to rank 12.
The 3 Guh Robots	Use the time machine and defeat the 3 bots another time.