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