Dragon Monster
Work your way up to B class. There is a battle called the Trial Cup in the 4th week of April. There is a dragon at this match. Defeat that dragon and get up to A class as fast as you can. When you get there you should sometime get invited to the August invitational. It is the 4th week of August. Defeat the black dragon in that and recieve the DRAGON TUSK as your prize. Breed the DRAGON TUSK with the DINO-NAGA and NAGA-DINO to get the Dragon Monster.
Henger Monster
To get HENGER you need to find the 5 DOLL PIECES during the DESERT EXPEDITION. Next,get your monster to A class and you will be invited to the WINTER INVITATIONAL with the DOLL HEAD as the prize. After you win, Tesca will put the 5 pieces together for you and give you the CLAY DOLL. he explains that you need to take an intelligent creature (550-999), along with the CLAY DOLL, to the previously unreadable STONE TABLET in the DESERT EXPEDITION.
After reading the TABLET, that monster will have a circular mark on his back. combine that creature, along with any other one and use the CLAY DOLL. HENGER has high STR, SKI, SPD, INT and lives for 6-9 years.
Magic Monster
First you must find a pure Gali and a pure Monol then combine the two and add the item Old Mirror (which you can get on an expedition with Karn.)
The lab man will say this is a bad combination, but go ahead with it. After they are combined, you will get the Magic monster.
Nya Monster
This is pretty simple to do. You just have to get to about the year 1026, checking the items shop periodically to get him to reveal his new items to you. The sixth or seventh new item he will get is called the cat doll. buy one for 1000G and use that when breeding any two monsters. You will receive the coveted Nya monster.
Secret Song
Put the CD in your CD player. Skip to track 2 and play it. You will be rewarded with some extremely bizarre music.
Shades
After breeding an ape monster, you can put in a Billy Joel greatest Hits CD and you will get Shades, a monster with excellent stats.