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