Size Doesn’t Matter is one of the 37 different Pet Battle World Quests that give credit towards Battle on the Broken Isles, which grants  Pocket Pet Portal. This battle is NOT part of any criteria for Family Familiar. 

Blottis is a single Epic pet encounter found on the Eastern beaches of Azsuna. He’s only available to fight when his world quest, Size Doesn’t Matter, is available.

Poison Fang
Body Slam
Rain Dance

Consider using Beast pets with Flying abilities, such as a Lurking Owl Kitten with Quills and Feathered Frenzy.