These avatars are found randomly.

Random when completing an Anagram Sam puzzle..
Random when using a Booster on your pet..
Have your pet turn bronze at the Operation Portal or Whirlpool.
Post a message on your club chat board.
Random event when visiting the Christmas Tree in Biala.
Lose an item in a random event.
Find the Bolimo in the Open Graves
Random when depositing 100,000 marapoints in your bank account.
Have your pet change into a Digital Equilor at the operation portal.
Take your pet to Eleka Fountain and gain a Magic Stat.
Win Eleka Tombola Stamp from Eleka Tombola
Random when picking up an enchanted plushie at the Plushie Machine.
Random when setting up a new trade.
Look up anything using the search box.
Random event when riding Fasoro Falls.
Find an item in a random event.
Win the Fruit Machine jackpot.
Test Your Strength game when you win the book.
Your pet needs to gain a charisma stat at the Guillotine.
Win a Code from a Traveller Quest.
Win the Stamp from Lush Tombola.
Find marapoints in a random event.
Random event when using the Operation Portal.
Random when picking up a plushie at the Plushie Machine.
Pay your power bill at the Power Station
after getting the bill in a random event.
Donate items from the Advent Calendar to the Pot of Gold.
Random event when riding Murfin Madness.
Random when buying a rubber duck from the toy shop.
Gain a pet stat from the Statue in Simeria.
Random when when attempting to pull the sword from the stone.
Random when using the Tanning Salon.
Win a Tombola Stamp at Tombola .
Random event when training your pet at the Gym.
Trash Fairy game level 7.
Pick up a bug minipet from the Trash Heap in City Sewers.
Win a Doomed minipet from Undying Fairy game.
Win Undying Stamp from Undying Tombola. Random when using the Whirlpool.
Bet on Newth No. 3 and win at Newth Racing.
Random when posting Yum on a club chat board.