To unlock this achievement, you will need to export around 3,000 units of rare metal, and the only way to do it before Sol 100 is with the space elevator. So now you know, in a nutshell, what you have to do. Here is how to go about it.
The best commander profile for this is Astrogeologist. It has two great advantages: extractor production is increased by 10 percent, and the Deep Scanning tech is unlocked. I found a fantastic starting location - it is 11S 162W. In sector J2, there are two very high grade rare metal deposits only a few feet from each other, containing 2,900 units between them. You can plop a basic dome down and get to work, with a vista, a research boost, and two water deposits as bonuses. Additionally, there's another very high grade rare metal deposit with 1,500 units one sector over, and a couple of lesser deposts in the neighborhood as well. Oh, and this map has no cold hazards, and meteors and dust hazards are very rare. This spot is Heaven, honestly.
With such an advantageous setup, you can probably figure out how to get the achievement yourself, but if you want to know what I did, I loaded up on geologists as much as possible and had as many colonists working in the extractors as much as possible. I started out with two, and by around Sol 30, I had one on the third very high grade deposit, and eventually I had two extractors apiece on the three very high grade deposits. When I was able to build a university, I trained nothing but geologists. For around 50 sols, I had no engineers or officers, and only a few botanists, medics and scientists. I imported all of my advanced materials and most of my food, and I outsourced much of my research. I emphasized engineering techs, to unlock the space elevator as soon as possible, as well as anything that increased the rare metal extraction rate, including Plasma Cutters (engineering), Fueled Extractors (robotics), Extractor Amplification (physics), and Productivity Training (social). I never built an ordinary metal extractor - there's more than enough metal on the surface, collectible by rovers. You'll also want to research techs that improve your rockets and drones. I was exporting 30 or 60 rare metals every 1 to 3 sols for most of the game. I researched the space elevator on Sol 79, built it in 80, and starting Sol 81, exported 230 to 360 units every sol, with the elevator making two trips most sols, and 5 rockets going back and forth continually. I unlocked the achievement on Sol 87.
"But what about the other ways of making money," you ask, "like tourism and the corporate office?" Yeah ... those pale in comparison. You can use them, but come on ... it takes 90 tourists taking up your living space, using your services, breathing your oxygen, etc. to get you as much income as one payload of trouble-free rare metals. The corporate office is better than tourism, but it still won't get you this achievement without tons and tons and tons of rare metals.
To prove my point, here's how I made my $100B by Sol 87:
$87.60B - 2,920 units of rare metal
$1.51B - corporate offices
$0.82B - 82 tourists
$10.07B - everything else (random events, anomalies, mystery, etc.)