Automatic training
After selecting the type of training (for example, trampoline in Morx Forest), rapidly press X. Your monster will perform the training process by itself, and most of the time will win if it is healthy.

Secret monsters
Use the following CDs to create secret monsters:

Lunar: The Complete Silver Story (Disc 1) - Game - Desert Hengar
Lunar: The Complete Silver Story (Disc 2) - Game - Legendary monster
Monster Rancher 3 - Game - Moochi
Spyro: Year Of The Dragon - Game - Ice Gitan
Ace Combat 4 - Game - Desert Karakarakkung
Armored Core 2 - Game - Robot
Suikoden 2 - Game - Forest Raiden
Tekken Tag Tournament - Game - Wrestling Moochi
Fantasia 2000 - DVD - Joker
Magnolia - DVD - Frog
Men Of Honor - DVD - Merman
Bob Dylan: Greatest Hits Music - CD - Marin
Dave Grusin Music - CD - Koronit
Chrono Cross (Disc 1 or 2) - Game - Strange Fenril
Digimon World - Game - Forest Hare
Final Fantasy Games - Game - Fairies
Front Mission 3 - Game - Sea Octipee
Train: Drops Of Jupiter Music - CD - Robot train
Gungriffon blaze - Game - Moochi

Note: Grampa Bragman will have to do research on the monster before you can get it.

Jokers
Train in Goat for awhile to get an item that will let you unlock Jokers from CD/DVD.