After I got this achievement (beat the game in under 8 hours), I looked around and was a bit surprised that I couldn't find an in-depth guide to getting it. (Aside from YouTube tutorials, but personally I hate those.) This seems like the proper place for such a guide, so here goes. This will be a long post, but I'll try to use spoilers so it's not too obnoxious.
My build is designed to be "low stress," but this does not mean "no stress" . I calculated it to finish research in around 5.5 hours, and launch the rocket at the 6 hour mark, giving 2 hours of slop. In the run where I got the achievement, I actually launched the rocket at 6:57, so I was glad I had that padding. It proceeds in two phases, roughly: 3 hours of frantic constant building, with lots of pausing to consult screenshots, followed by 4 hours where you kill some spawners, make concrete, and do other small tasks but mostly sit around and wait.
You can beat the game faster, of course, but my build is pollution-limited so that you shouldn't ever have any alien attacks, assuming you're playing with a "very big" starting area. Note that it's pretty finely tuned - everything is designed to finish at about the same time. Thus, although it might be tempting to try and speed things up by adding an extra assembler, or upgrading things to yellow assemblers, this won't actually help the launch of the rocket, and in many cases will slow things down by causing a resource shortage. If you want to go faster, you'll need more than the 1600 plates/min that a single basic transport belt can provide, which means you'll have to run the numbers and come up with a full design yourself.
If you want a roughly step-by-step guide, use the following map exchange string, so you can follow my screenshots exactly. (I'm not sharing blueprint strings because they would be useless - this build never researches blueprints or any kind of robotics.) If you want a more spontaneous approach, then I recommend very rich resources of all types, a very big starting area, and high frequency stone/coal, with the rest very high frequency. And you'll want to re-roll until you get a good initial clustering.