Here is the full list of all 19 Amazing Superhero Squad achievements.
Finish all the events of the plot
Successfully accomplish all the events of the day
Successfully accomplish the events aimed at getting the super out of depression
Hire a detective
Hire a new super
Accumulate more than 80,000 credits at the end of the day
Distribute all supers to events
Send compatible characters to the event
Send non-compatible characters to the event
Open 1 exotic solution
Successfully complete the first week plot
Successfully complete the second week plot
Successfully complete the third week plot
Lose a superhero at an event
Fail all rat invasion missions
Ignore 10 events
Hire 5 sups
Fire the super
Solve the super's problem