"Get to sector 8 without your ship's net oxygen levels exceeding 20 percent (starts after the first jump)."
For this achievement to work, you must shut down the oxygen in 80 percent of the rooms on your Lanius Cruiser until you reach sector 8. Because every ship starts with 100 percent oxygen, you must vent before your first FTL jump. If your first jump is made with above 20 percent oxygen, the achievement cannot be obtained for that run.
This achievement is made easiest by simply turning off the O2 system, venting the ship completely at start (killing off your non-Lanius crewman, who could potentially be brought back infinitely with the onboard Cloning Bay if you cared to keep them), and then getting to sector 8 without ever turning on O2 again.
If you don't follow this tactic, be wary of rebel auto-hacker ships: When your oxygen is operational, a hacking drone to your door system can very quickly bring your oxygen level above 20%.
The game is completely winnable with only 2 Lanius crew, so long as you steer clear of crew-killing random events - like Giant Spiders unless there is the possibility for the crewman to be revived at the Cloning Bay. And if you find more, then all the better. The only foreseeable hardships with few crew is boarding and fires, both of which are dealt with proficiently by having no onboard atmosphere.
ATTENTION: This Achievement is bugged in some versions - you may not save & quit during the achievement run. Fortunately, it is has been fixed in the most recent version.