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.
Random Access
Database unlocked
Sarah has logged off and crossed the road
100% of database accessed
He asked me to kiss him
The Wind and the Rain
75% of database accessed
It's a snake and an apple
Fuck!
50% of database accessed
Not all games have winners and losers
Rapunzel's story
Masterchef