Here is the full list of all 19 Who Did It? achievements.
Solve your first case
Solve 5 cases
Solve 10 cases
Solve 15 cases
Solve 20 cases
Solve 25 cases
Finish the Story on any difficulty
Solve your first Detective difficulty case
Solve 10 cases in the Detective difficulty
Solve all cases in the Detective difficulty
Read all the hints on a case
Fail a case by running out of time (Detective difficulty only)
Fail a case by running out of strikes
Solve a case on your first try
Solve a case without using any hints
View your statistics
View the credits
What did you expect to happen? (secret)
Solve a case in less than a minute (all difficulty's except detective)