This is the last milestone in the "Alien Colonists Encountered" statistic and is obtained once you have spoken to 80 aliens (not animals). You can check your progress by pressing Start and looking at the Milestones screen. It is near the second entry in the "Journey Milestones" section.
The easiest way to do this is to visit all space station. There should be plenty of aliens there (about 10 per station) to talk to so you should unlock this fairly early in the game. Shop keepers don't count for this, only the aliens standing around. You can also find encounterable aliens on planets either at trade post or other landing pads.
Note. The achievement tracker (percentage complete on the Xbox) does not work for any of these achievements. The achievement is for reaching the target milestone and being awarded the title.