Here is the full list of all 10 Firewatch achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Completed Day 79
Got attacked by a raccoon; probably didn't get rabies.
Listened to the tape of "Ol' Shoshone." Cavorted among the aspens.
Completed Day 77
Got stung by a bee. It happens.
Completed Day 76
Completed Day 2
Adopted a turtle as a pet. The average lifespan of a box turtle is fifty years. It will outlive you.
Filled a disposable camera with photos.
Completed Day 1