Start with the Broken Shackles Origin, and make a tiny galaxy with no opponents, no fallen empires and no pre-FTLs. (Some will spawn as part of the origin)
Build up your empire fast, and focus on gaining as much political power as possible while doing so.
When the galactic community forms make sure you get the ban organic/synthetics slave trade resolutions passed.
Hopefully the rest of the galaxy will not be in violation of the galactic law, and you can just invade the pre-FTLs to bring them in to your empire and the achievement should fire.
If any of the other empires are keeping up slavery despite the galactic law, you might need to prepare to subjugate/conquer them first.