Firstly, you'll need to get a slime key by bursting a Gordo Slime.
This will unlock Jelly Belly Burst. (See my guide for this achievement)
Once you have one of those you'll need to get to the door. From the Ranch continue straight ahead until you find the first opening where tabby slimes will spawn. In this area there will be a small cave to the right with feral Pink Phosphor Largos. If you continue to the end of the cave there will be a slime door. If you open this door you will get the achievement! If this is your first slime door you'll also get the Open Says Me achievement
Here's my video for all achievements if you'd prefer. Skip to 5:12 for Mine, All Mine.