Here is the full list of all 10 Sickness achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Spend eternity with Sara
When things get messy, neglect your duties
Cohabitate with Misa
Give up everything to stop history from repeating itself
Turn the tables while being seduced
Kill Mr Roth while he's indisposed
See this season's biggest blockbuster
Attend counseling
Turn down the opportunity of a lifetime
Fail your first paid kill