Successfully complete one of the following tasks to get a trophy:

Xipe Imoon Trophy (Bronze): Award for exemplary completion of an Imoon nebula. 
All levels of the nebula must be completed with a minimum score achieved on 
each to win this award. 
Ymir Imoon Trophy (Bronze): Award for exemplary completion of an Imoon nebula. 
All levels of the nebula must be completed with a minimum score achieved on 
each to win this award. 
Zeus Imoon Trophy (Bronze): Award for exemplary completion of an Imoon nebula. 
All levels of the nebula must be completed with a minimum score achieved on 
each to win this award. 
Imoon Agamemnon Trophy (Bronze): This is the award for the successful 
completion of the first level of the Xipe nebula. 
Imoon Technician Trophy (Bronze): This award is for the first successful 
building of a tower upgraded to level 5. 
Imoon-Bane Trophy (Bronze): Awarded for killing a huge number of Insectocytes. 
Imoon Survivor (Bronze): Awarded for surviving for an impressive amount of 
time in any Vengeance Mode level. 
Command Degree Trophy (Bronze): Awarded for completing all of the tutorial 
sections of the game. 
Command Credit Trophy (Bronze): Awarded for earning a significant amount of 
credits during your levels. 
Command Skill Credit Trophy (Bronze): Awarded for earning a significant amount 
of credits during your game using Command Skills. 
Imoon Conqueror (Silver): This is the award for completion of all levels of 
the three Imoon nebulae. 
Imoon Artisan (Silver): Award for mastery of technology. This is achieved by 
researching and building all tower types in the game. 
Imoon Admiral (Gold): This is the award for completion of all levels of the 
three Imoon nebulae without any damage to mining operations.