I believe there are a few ways to get Jade Oni, but i believe these are your only options.
1.hatch anything with a Jade Oni pet and get truly lucky. This is not a recommendation if you dont like to gamble, but it is the way you want to get the pet.
2.Farm the Jade Oni. i heard that if you kill the jade oni and are lucky, you will get this pet as a drop. just bring friends and hope for the pet. this is my choice because either way you can get some neat stuff before OR after you get the pet.
3. buy the pet with crowns at the wizard city pet shop. I DO NOT recommend this at all since this would be a waste of crowns. however, use it if my first choices dont work.
with just enough luck and practice, you too can get a jade oni pet. hope i helped!