I believe the key to this achievement is to select the game rules "Amateurs" (no specialist applicants) and "More Applicants" (500 additional applicants). This will give you an essentially unlimited supply of flawless youth and adult non-specialists to train in your universities for the entire game. You might be able to unlock the achievement with only one of these two rules active. I don't think it's possible if you don't select at least one of them ... or if it is, you'll be making it pretty hard on yourself.
Japan only gives you one rocket, so the Rocket Scientist commander profile looks pretty good. Then again, I chose random, got City Mayor, and put my extra $2B funding toward a second rocket ($3B), so the commander profile probably isn't all that critical.
Japan has a sponsor goal that is helpful toward getting this achievement: after you build a polymer factory, machine parts factory, and electronics factory, you get a Martian University prefab. And yes, the small versions of the machine parts and electronics factories will work for this. So, by ordering those two small prefabs early on and either ordering or researching the polymer factory and building it, you can get your first university up pretty early - even during the founder stage, if you really want to get a leg up.
Of course, you will want to research the Martian University pretty soon, and also research Martianborn Adaptability (biotech) to speed up the universities. Early on, I was hand-selecting my university students to be martianborn because I was anxious to start putting some numbers up, but before long, I got tired of doing that.
Don't worry if you get off to a slow start. By Sol 35, I only had 9 graduates, but eventually, I had 4 universities working at 2 full shifts each and was cranking out 5 diplomas every sol. I had my 100th graduate in Sol 65 and got the achievement in Sol 85.