Note: you must finish a storyline in one area for another story to begin.
If you are waiting for an event to happen, try going back to any area where you have been involved in a storyline, and make sure you are really finished, then go back to the area you need to be in to unlock your monster. The most commonly unfinished storyline is Takrama's Golems. It's not over until you have been congratulated several times during the six months following the defeat of the Golem. This is critical for unlocking Zan and Joker.

Baku: Available from the start of the game.

Beaclon: Available from the start of the game.

Colorpandora: Available from the start of the game.

Dragon: Locked discs give a message about legendary power.
Get a monster to S rank by beating the official A level tournament. You will not be given any notice that they are now unlocked.

Ducken: Available from the start of the game.

Durahan:Locked discs give a message about legendary power.
Get a monster to S rank by beating the official A level tournament. You will not be given any notice that they are now unlocked.

Gitan: Available From the start of the game.

Golem: Available from the start of the game.

Hare: Avaialable from the start of the game.

Hengar: Available from the start of the game.

Jell: Available from the start of the game.

Joker: The locked Joker discs give a warning about a monster being too powerful.
Unlock the Goat (underwater) area. Continue training until you meet Kai. This may take a couple of game years. Eventually (perhaps in the first week of August) he will give you an item and invite you to a match at night in November to unlock Joker. Hang around in Goat until you discuss this with Ms. Jenna when she shows up. She'll mention Grandma Mosha in Morx. Go to Morx, then talk to Grandma Mosha. You'll get prompted if you want to go fight, select "yes." Then in the second week of November, be in Goat, and choose "yes" to go to the tournament. Then you must beat Kolbain, a Joker. (Lif 412, Pow 506, Int 534, Spd 486, Def 248) If you lose, your monster loses lifespan(!), but you can try again in future years if you're in Goat on the second week in November. Once you win, you must go into to town and talk to Grandpa Bragma. Then Joker is unlocked at the shrine. You need to go to town right away! If your monster dies before you go to town, you will not be able to unlock the Joker, ever. So make plenty of saves in advance of and during this event.

Lesione: Available from the start of the game.

Mew: Available from the start of the game.

Mocchi: Available from the start of the game.

Mogi: Available from the start of the game.

Momo: Available from the start of the game.

Naga: Available from the start of the game.

Octopee: Available from the start of the game.

Ogyo: Available from the start of the game.

Pancho: Beat an B level official tourney, so your monster is at A level, and these will now be available in the shrine. You will not be given any notice that they are now unlocked.

Pixie: Available from the start of the game.

Plant: Available from the start of the game.

Psiroller: Available from the start of the game.

Raiden: Avaialable from the start of the game.

Suezo: Available from the start of the game.

Suzurin: Available from the start of the game.

Tiger: Available from the start of the game.

Zan: Locked discs give a warning about an unknown breed.
Visit the Brillia area. You'll be meet some local people, and battle their monsters. Then you'll battle a bad monster, and hear that it's modified. Just keep playing, and eventually you'll be challenged by a Zan wearing accessories. Battle it, win/lose/KO does not matter -just battle it. The accessories will disapear, and it will bow down to you. Then the Zan and owner will walk away. The next week, they will return with a saucer stone for you. Go to town, and talk to Grandpa Bragma. He will say he needs to research the stone, and will get back to you. He won't. Just go to the shrine now with a Zan CD/DVD. You may now get Zan at the shrine.

Zoom: Available from the start of the game.