Atomicrops

The Golden Goose is a random spawn; there is no guarantee that it will show up in your run. But some tips that I can give are that:

1. If you kill it, you should get a rare seed (typically a tree) as a drop and you should see a golden feather appear.
2. While doing a daily run, I had the Golden Goose appear twice in that run.

When you come up on it and attack it, it will try and run away and bury itself into the ground, so try and have ranged weapons that does a good bit of damage.

Edit: I got this achievement shortly before the Doom and Bloom update came to console.