The hardest thing about this achievement is actually unlocking The Positronic Brain breakthrough. I'd played around 8 games and hadn't discovered it once.
Then I found this site -
http://survivingmaps.com/ Here you can find map co-ordinates based off resources, disasters etc. but most importantly you can specify a breakthrough and it'll then give you the map co-ordinates where you can unlock this tech! (Not sure how reliable it is but I got it on the 1st map I used)
I played at
4S 110E and Positronic Brain was about the 3rd breakthrough that I unlocked.
I recomend playing with fast scanning enabled (As well as other preferable options that don't disable achievements; fast rockets, extra production, prefab colony & extra applicants)
Once you've unlocked it you then need to build the Drone Assembler which needs 5 electronics to make 1 biorobot (On the above map it also had the breakthrough to make them from 5 normal metal instead)
Build at least 50 across your Drone Assemblers and then designate a dome for the biorobots. When you filter by traits Biorobots are listed under Perks. Enable it in a dome with at least 50 vacant homes and then deny that perk on all of your other domes and this should pop once the 50th moves into the dome!
Edit: Just played another map from the website with Positronic Brain (5N 114E) and I discovered the breakthrough fairly quickly so the website seems fairly reliable!