I have no Everything pet because I had no idea the concept existed when I first started playing. Instead I just randomly assigned individual categories for my pets to collect based on personality or costume. Not at all efficient, I know.

Babyface:
-Toys

Dralmor:
-DVDs

Fat:
-Gourmand

Nacre:
-Battle / Stats pet
-Spells
-Instruments

Pepsicola:
-CDs

Willoughby:
-Books / Newspapers / Magazines

XV:
-Transformations pet