I don't know what level you are but, most hidden bosses drop pets. Like in Olympus and Castle Darkmoor. In Polaris bosses drop pets a lot too. Hope this helps
I am looking for a new pet, and I was wondering who I can fight that drops a pet. Does anyone know that can tell me?
tons of bosses drop pets, though the drops are incredibly rare. i'll list some of the ones i've gotten before. as well as where i got them:
(since you didn't mention your level or which worlds you have access to, so i just included all the ones i could think of)
life troll (krokopatra, krokotopia>tomb of storms) beastmaster's eagle (ludos the beastmaster, polaris>urville station>kennels) mountain yeti (the rat, polaris>horizon hold) intrepid seal pup (warlord minak, polaris>borealis peaks>jewelled slopes) red cap (ullik, grizzleheim>helgrind warren>hall of valor) rooted grimoire (izft, krokotopia>upper zigazag>house of scales) life scarab (plague oni, mooshu>shirataki temple) soulful knight (sir blackwater, wizard city>castle darkmoor)
those are the only ones i can think of at the moment. i also have 8 houses with pets in them (and that's just on one wizard), so i can have a look through next time i'm in-game.