So first and foremost you need to purchase the Slime Lab; this will cost you 10,000 newbucks. Next, you need to purchase the #1 Slime Stage blueprint which costs 3,500 newbucks. Finally, you need the following components put into the Fabricator:
25 Pink Plorts
8 Indigonium
8 Spiral Steam
1 Royal Jelly
You get Indigonium from the Indigo Quarry using a Drill (any as it is common to that area). You get Spiral Steam everywhere with a Pump, but be aware that it is an uncommon drop. And finally you get Royal Jelly from an Apiary anywhere but the drop is rare.
Go to the Fabricate Gadget station and fabricate it (press
). Press
to enter Gadget mode and place it somewhere. If you want to do this in a controlled environment built a Corral near the lab and place the stage nearby. Create your own tarr by feeding a largo a plort that it does not produce and you'll have your tarr. Pick it up and place it on the stage, achievement unlocked.
Edit: To drop just press
instead of
which fires it off instead of placing it.
Edit 2: Here's a video I did if you need a more visual medium to understand what to do: