After beating the game(s) (1 and 2) there are a number of special vivosaurs that you can get by doing certain tasks or defeating certain characters.
Igno- You can get Igno after beating Saurhead in the Fossil Stadium locker room three times.This is kind of a marathon because he will challenge you three in a row with a different team each without you being able to change your team.
- - You can get Guhnash's three brains by defeating him again by using Dr. Diggins's time machine. This is the same exact fight as the first one.
The 5 Chickens- Train ALL 100 vivosaurs to RANK 12 (evil, isn't it?)
Fossil Fighters: Champions
Frigi, Igno- Nintendo Wi-Fi Connection. On the main screen, choose "Multiplayer". then go to "Bonus Data" and connect. Your vivosaur(s) will be on the fossil lawn. Collect them and they will be automatically revived and sent to your VMM.
Dinomaton, Duna, Raptin, Dynal, Salada- Special quests will be unlocked after getting messages through Nintendo WFC. The messages can be found in fossils on the Fossil Lawn.
Zongazonga, Z-Rex, Z-Tricera, Z-Elasmo, Z-Ptera- defeat Zongazonga for the second time after beating the game
B-Lambeo, B-Rex, B-Plesio, B-Ptera, B-Jara, B-Tricera, B-Brachio- Defeat Cole (Ilium Village), Lola (Ribular Town ), and Lester (Cranial City (in the Fossil Guild)) for the second time. Each one unlocks two of the aforementioned vivosaurs and the last one unlocks three
Tonzilla- defeat Robinson after beating the game at the end of the Bonehemoth