Here is the full list of all 13 Her Story achievements. It takes around 3-4 hours to unlock all of the achievements on Windows.
Sarah has logged off and crossed the road
He asked me to kiss him
Rapunzel's story
The Wind and the Rain
Masterchef
50% of database accessed
75% of database accessed
100% of database accessed
Not all games have winners and losers
Random Access
Database unlocked
It's a snake and an apple
Fuck!