Surviving Mars

This isn't as hard as it sounds. You'll need to make a dedicated science dome preferably in a dome thats recieving a science boost (although don't panic if thats not available as I got it without it)

I built a medium dome with 3 Hawking Institues and a Network node all fully staffed across 3 shifts with scientists (Use the extra applicants perk to get extra applicants)
I also had the Research amplification enabled on all 4 buildings.
The rest of the dome was just appartments, a grocer, diner & spacebar.
The only other science building I had was 1 of the outside research buildings that Europe gets although this wasn't very well manned in the end as I had moved all scientests to my science dome.

This got me to just over 9k research a sol then I outsourced 1k from Earth which put me over the 10k mark and unlocked the achievement!

If that doesn't get you to 10k then you can build more Hawking Institutes in another dome. Or the Omega Telescope can boost your research.

If you really want to go OP then you can use http://survivingmaps.com/ to find a map with the Superconducting Computing breakthrough tech on it. Once you've unlocked this build the Artificial Sun and that should give you around 4k research points a sol!

Network Spire is near the end of the Robotics tree. Research amplification, Omega Telescope & Artifical Sun are at the end of the physics tree and the Hawkings Institute is in the middle of the Social tree.

I suggest playing with the modifiers prefab colony, fast scanning, fast rockets, increased production & extra applicants. No disasters or events is optional depending on your preference (Both can help or hinder)
None of these options disable achievements.