Here is a following list of pets currently in the game (or have been released at some point in the game) and they're pet Apptitudes...
Obtained from NPC'S or Quests:Woody Pig Type: Beast Aquired: This pet comes in the new player chests, can also be aquired from the lvl 15 pet quest from pet tamer Totto, or purchased from Totto for 150g. Apptitudes in Woodwork and Hunting
Dryadling Type: Nature Auqired: Randomly from the lvl 15 pet quest or purchased from Totto for 120g Apptitudes in Woodwork, hunting, and mining
Rubi Boar Type: Yasho Aquired: Purchased from Pet Tamer Totto for 120g Apptitudes in Hunting, Fishing, Mining
Jumping Squirrl Type Nature Aquired From Pet Tamer Kokko for 120g in the Divine Realm Apptitudes in Woodwork, Hunting, Mining
Battle Ground Tiger Type Beast Aquired from the Battle Ground Vendor for 300 skyline Pearls and 30k courage points Apptitudes in Woodwork and Hunting
Yaksha Ranger Type Aquatic Aquired from Outcast Merman at the entrance to the Dread Labryinth For a Yasho Essence and a large number of leaves Apptitudes in Farming and Treasure
Hades Watchman ? ?
Plump Toad Type Aquatic Aquired Randomly from the Free Lunch Quest from Pet Tamer Totto...has no apptitudes
Wild Wolf Type Beast Aquired Randomly from the Free Lunch Quest from Pet Tamer Totto...has no Apptitudes
MARKET PLACE PETS Stonus Protector Type Elemental Apptitudes in Farming Hunting Treasure
Kuzge Type Mutant Apptitudes in Woodwork Mining, Treasure
Cloud Tiger Type Beast Apptitudes in Woodwork Hunting
MuiMui Type Yasho Apptitudes in Fishing Hunting Mining
Jesse Type Celestial Apptitudes in ALL
Scorpus Ravager Type insect Apptitudes in Mining Treasure
Ghengis Kong Type Celestial Apptitudes in ALL
Checkers Type Celestial Apptitudes in ALL
Christmas Snowman Type Celestial Apptitudes in ALL
PET CAPTURE PETS Underworld Judge Type Ghost Apptitudes in Woodwork Fishing Mining
Night Owl Type Nature Apptitudes in Woodwork Hunting Mining
Little Deer Type Beast Apptitudes in Woodwork Hunting
Chubby Baby Type Yasho Apptitudes in Hunting Fishing Mining
Fire Rock Demon Type Elemental Apptitudes in Farming Hunting Treasure
CURRENTLY NOT AVAILABLE (unless through vendor stalls in Trade Realm)Lamb Chop Type Beast Apptitudes in Woodwork Hunting (currently not available..event pet is from is over)
Phantasma Type Delusion Apptitudes in Woodwork, Hunting, Treasure
Aissy Bear Type Beast Apptitudes in Woodwork Hunting
Fairy Diah Type Fairy Apptitudes in Farming Fishing
Chromawing Type Avian Apptitudes in Farming Hunting Fishing
Dystinor Type Avian Apptitudes in Farming Hunting Fishing
Silver Fox Type Mutant Apptitudes in Woodwork Mining Treasure (currently not available unless from another player in form of Fox Coupon)
Hell Fire Inferno Type Elemental Apptitudes in Farming Hunting Treasure