Gonna shimmy in here and dump a bunch of neat urban legend ideas on y'all.
Hakutaku / Bai Ze - Basically a large Chinese beast that knows literally everything, as I understand it? There's a lot of neat imagery of these if you do a quick google search.
Jersey Devil - "The creature is often described as a flying biped with hooves, but there are many different variations. The common description is that of a kangaroo-like creature with the head of a goat, leathery bat-like wings, horns, small arms with clawed hands, cloven hooves and a forked tail. It has been reported to move quickly and often is described as emitting a 'blood-curdling scream,'" says Wikipedia. Also lots of nice art on the internets.
Malora - headless equine thing, possibly mule, embodiment of a witch's lust? Idk I just like non-gory headless things and I like horses, eheheh.
Kelpie - beautiful horse that lives in the swamp, sometimes turns into a hot guy to lure people in, actually a freaky half horse half fishy thing that drags people down into the swamp and eats them. Gotta love it.
Manticore - I'm surprised we have no manticore pets yet! There's a lot you can do with these. Multiple different creatures on one body, lots of possibilities. Scorpion dragon lions I guess, ohoho.
Nguruvilu - literally "fox snake," the article says "Nguruvilus live in and are the cause of dangerous whirlpools which kill people who try to cross rivers. They make the water shallow on either ford, to encourage people to try to cross it making it seem safe. However, the only safe way of crossing a river with a Nguruvilu is by boat." Unsure if this is what Sea Borks are based off of? If so, ignore this one eheh.
Tatzelwurm - Front half of the body is that of a cat, back half is a snake. Freakyyyy. Alternatively, if the cat bit turns you off, you have
Lindworms, which is all dragon/snake.
Peluda - Porcupine dragon, basically? "Depending on the account, it had either an ox-sized porcupine-like body or a mess of green hair-like projections hanging from its body that were actually stinger-tipped tentacles which could erect into quills and have these poisonous stingers that it could also shoot off its body, a snake's scaly neck, head, and tail, large, tortoise-like feet, and a green color."
Crocotta - This one is pretty odd; it's essentially a dog/wolf thing with some deer parts to it and a really wide mouth with bone ridges instead of teeth. "Crocotta has the ability to imitate the voices of men to lure prey and described as having amazing strength, be as brave as a lion, as swift as a horse, and as strong as a bull and they cannot be overcome by any weapon of steel."
Catoblepas - Ugh this one gives me the creeps. We don't have many cow/bovine like pets, so this one might be neat; "said to have the body of a buffalo and the head of a wild boar. Its back has scales that protect the beast, and its head is always pointing downwards due to its head being heavy. It's stare or breath could either turn people into stone, or kill them." Plus that long-ass neck is just. Terrifying.
Hydra - Multi headed dragon, nuff said.
Qilin/Kirin - One of my favorite mythical creatures. I'd suggest you read the article because it's a good deal of information, haha.
Cerberus - Again, multi headed hell doge. Fun stuff.
Pixiu - Winged lion that wards off evil. o vo Might be a neat Hunter alternate form, if anything.
Ittan-momen - One thing we're really lacking is some inanimate object based pets. We have Tatterdems, and to some extend the -leef Evolutions, so this would be a neat one. Basically it's a long strip of cloth that can wrap around people and smother them. So cloth snake? To be honest I love the idea of either origami creatures or cloth based creatures, like the NPC creatures in the game Journey, if you'd like to look those up.
Bake-kujira - Ghoooost whaaaaale. Basically it's see-through, except for its skeleton. Ghostly pets are nice. uvu
Sphinx - Y'all know this one. Body of a lion, head of a person/personlike thing, tells riddles, ayy. Could make for some fun designs; of course on all of these since I know human features on pets are strange, with the exception of Quiksylves, so the human parts could be severely stylized.
Bahamut - GIANT whale/fish creature with the head of an elephant or boar. Basically whale with tusks that's like, really frickin huge and spooky.
Aqrabuamelu/"Scorpion Man" - Warriors with the bodies of scorpions and the torsos of humans/what have you. Basically scorpion-taurs. I love desert themed things and I think a scorpion pet besides that one we have that's like, mostly spider/mantis would be cool.
Wendigo - Could be a fun experiment pet; bipedal deerlike yeti creature that eats people and lurks in forests.
Ogopogo - Essentially Nessie! Surprised we don't have any loch ness based pets, or plesiosaurus or whatever you call them.
Ahuizotl - Funnily I think these animals were recently popularized by MLP or something like that but heyy these are super neat. Kind of a strange Aztec dog monkey creature with a hand on its tail.
Here's a nice example by deadrabbit13 on deviantart.Wondjina - These really really give me the creeps. Maybe it's the eyes. Anyway I figured it might be neat to have some kind of pet based off of cave paintings or ancient art? These are creatures that deliver monsoons. Cloud/rain spirits, kinda humanoid but that can be altered.
AND it's not a mythical creature (though it is certainly very heavily involved in New Zealand's legends), I would love a pet based off of a
Kiwi Bird. They're just my favorite things, and they're so darned cute. ;v;