How do I obtain a Zentu??

The FAQ guide link on the News page will tell you

You can go to the Zentu Baths in Shengui Guo and adopt one. You'll need an open pet slot, and the kind you get depends on whether you go while it's daytime or nighttime in Shengui Guo. You can refresh the page to change the male/female aspect until you get the one you want.

Or, if you want to turn one of your existing pets into a Zentu, you can buy an elixir for the color you want from the shop Five Seven Five.