Green Knight
The Shrine, an in-town destination, is where you can go to unlock monsters. You'll be presented with a text-input screen. Use any word that you can come up with, and it will result in a monster. For example, the code Hobo results in a powerful, green Lezaal-type monster, number 326.
Golden Monsters
There are a handful of golden monsters that you can unlock. They're just like regular monsters, but with a gold hue. Head to the shrine and use the codeword "night1" to unlock a Goldie. To unlock a Golden Caraban, input "Samurai" at the shrine. To unlock a golden Mustardy, input the word "skills". Use the word "Shining" to get your golden MerryArrow. The word "chrome" earns you a Golden Warabi. For a golden Titan, "ultra," and for a Kuku, "cut." All of the codes are case-sensitive.
Special Monsters
If you're looking for a specific monster, you will need a code. These special monsters have higher stats than most, which will help you rise through the ranks. For example, to unlock a Justin, "Roko." If you're looking for a Marine Mew, try "jeds." There are many others: Metal Octy, "ryu"; Golem, "PAI"; Crab Zuum, "TK"; Ballad, "Pale"; Ace, "Rika"; Mocchi, "miss"; Peng Moch, "Geni"; Raven, "Will"; Remus, "Leaf"; Ryuon, "Lion"; Yuppee, "Snow"; Yuzumoochi, "K9dG"; Lesione, "dawg"; Mochikung, "SK8". These codes are all case-sensitive.
Rabiroller
The Rabiroller-type monster is otherwise hard to find, but you can very easily make one with the right code word. In this case, use the word "cabbit." Any word with the letters "abbit" in them will produce a Rabiroller.
Diva
The Diva is one of the most powerful monsters you can get your hands on, and while this dragon-type monster could eventually be discovered through breeding, you can save yourself time by going through the shrine. Type in the code "Infinite" and you will find yourself in control of a Diva.