Some monsters, although few, can only be caught by breeding. They can't be caught from foreign masters, and they're incredibly rare. If you've got one of these monster 'jewels', you're lucky!

Goldslime
Coatol
Divinegon
Kingleo
Rainhawk
Rosevine
Herbman
Armorpion
Akubar
Jamirus
Durran
Evilpot
Goldgolem
Whiteking
Dracolord 1
Dracolord 2
Mirudraas 1
Mirudraas 2
Sidoh
Hargon
Baramos
Zoma
Pizzaro
Deathmore 1
Deathmore 2
Deathmore 3
Esterk
Mudou
DARKDRIUM (The king of rare!)