Donut County

In the final level while flying the quadcopter, follow the long anchor and chain in the sky up to its source where you'll find TK and some other raccoons hanging out in their skyboat.

While in the biolab at Trash King's HQ, collect the snake and input the following commands in order:

↑, ←, ↓, ←, GRAB.

If done correctly, a cutscene should play showing the vault door opening. Play through the level normally and head to the main hall, the security door, and finally the vault with the new hole that spawns.

The recipe for Chef's secret soup is located in the Trashopedia:

"2 shakes salt, 3 shakes pepper."

While in Cat Soup, collect the soup and make small circles to avoid the cockroaches that will spawn or from feeding the soup to the blue bird too early. If they touch the soup you'll need to start over.
You can collect multiple shakes of salt or pepper each time they circle around on the carousel, just be careful to avoid the bugs.

Once you feed the correct recipe to the bird, it'll tear up at the taste and the achievement will pop.