Now and then, I get "achievement complete" popups in-game. How can I view my achievements? I'm playing the Android version.
There is no way to view your achievements from in the game, not even if you are playing the PC/Linux/OSX builds.
The only way to view achievements (and I believe the only reason the achievements even exist in the game) is by running the game through Steam, and listing them there.
However, if it is important to you, you can get a fairly good estimate of how many achievements you have completed.
There are 17 total achievements in the game, and 13 of them are "Research Achievements":
These are completed once you have completely researched a species. If you flip through the pages in the "Research" area, you will be able to see which ones still need to be researched further before you can "get" the achievement.
The remaining 4 achievements are unlocked progressively as you go through the game, and if you have explored every cave and finished the game with the "ideal ending", you should have gotten all of them along the way: