The following avatars all need you to own a certain type of pet.
Either certain species, colour or training levels required.

Own an Angel pet that has watched Angels then view it's DVDs.
Use a camouflage costume on a pet with over 30 HP.
Use a checkered costume on a pet over level 30.
Feed a Cheese Marapop (not Diet) to a Cheese Fasoro.
Own a level 51+ chibs, battle with it and then view it's profile.
Own a Chocolate pet and feed it any chocolate.
Own a clown pet and let it play with a balloon.
Use a dark costume on a pet with over 30 strength.
Equip a regular Dasher to a snowy pet and view it's profile.
Train your pet to level 26 in defence at the gym.
Equip a Staff of the Devil to a Devil pet and view it's weapons.
Have your equilor turned digital by the Operations Portal or Whirlpool.
Own an Elf pet, have an Elf costume in your inventory, click on it and click "use" but don't use it.
Feed a junk food item to your Fat pet.
Attach a Fild to any limited edition pet.
Equip a Flaming Hammer, Flaming Shield,
Flaming Axe and Flaming Fan
to a Fire pet.
Complete level 50 in Music with a hammy attached.
Own a gold reese, make it 100% happy then view it's profile.
Complete level 152 in history.
Use a Hobo Costume on your Chibs or Osafo.
Use a love costume on a pet with over 30 magic.
Complete Level 27 in Maths.
Feed sushi to a mermaid jessup.
Use a Old costume on a pet with over 30 Defence.
Take a photo of your Shaved Walee at the Photo Parlour.
Own a pirate pet and view it's profile.
Put a Plushie Costume on a huthiq.
Have a feliz in jail and free it.
Own a purple pet and view it's profile.
Paint your pet with a radioactive costume.
Attach a Rainbow Zax to a Rainbow pet.
Feed a red gumball to a red addow.
Accept a Robot pet through the Pet Exchange.
Put a Royal Costume on your pet.
Own a Zombie Yakubi.
Train your pet to level 52 in Science.
Paint a chibs with a seasonal costume.
Operate on your space azul at the Operation Portal in Ziranek.
Train your pet to level 77 in Sport.
Let your starry pet play with a rarity 7 star.
View your Stoneage pet that is level 49 or higher.
Visit the Ice Caves. with a Superhero pet.
You will need to have completed the Christmas Treasure Map
before you can visit the Ice Caves.
Have 3 Toddler pets on your account and view your pets.
Feed a Water Crystal to a Water pet.
Use a healing potion on any wizard pet.
Attach a zax to a pet of the same colour.