Limited Edition Pets (LE's) are avaliable through a few different means.

Collecting the whirlpool map: There is a small chance, if you have the complete whirlpool map, that you will have your pet turned into any species (including LE).

Temple of Transmogrification: To complete this temple you need to give it hieroglyphics, after 30 levels you can transform your pet into any species!

Missions: Missions are probably the easiest way to get an LE pet. Here is a mission guide: http://www.maraforce.com/guides/missions.html Each mission has 30 levels to complete, and you are rewarded with an LE potion at the end of it.

Potions: Other users may sell an LE potion (which you then use on your pet), or if you're lucky enough, you may be able to restock one in the potions shop.