The achievement is pretty self-explanatory but I'll give some tips having now done it myself:
I would recommend saving this achievement basically for last in terms of item progression and finish out your Nuclear armors/tools before completing this as the the 100 Nuclear Machinery it will cost to upgrade 100 crafting structures is pretty expensive in terms of materials (requiring 1 Cosmic Steel, 1 Nuclear Fuel Cell, and 1 Onyx Relic per craft) and the perks on the Nuclear tools can help you quickly farm some of the missing materials you need (for the fuel cells especially) if you're short. Also, I don't really see a reason to be running, for example, 100 Nuclear Forges. While the double item output is nice, the amount of fuel necessary to keep them all going seems like it would be unmanageable (not to mention there's nothing to really grind for past this point.)
Anyway, once you've crafted your 100 Nuclear Machinery, hit a Shrine and grab the 50% building cost reduction buff. From there, I found it easiest to just mass produce Forges as they only require stone (with the building cost reduction buff, I think the final few forges were in the 5-10 million stone range which barely made a dent in the 800 million or so I had by this point). I specifically used the Obliterator and Landfill to create a big clean tract of land to do this on at the top of the map, but you could do this bit by bit all over the entire map if you didn't want to go through that trouble.
From there, just use your 100 Nuclear Machinery on your 100 Forges, and the achievement is yours.