Here is the full list of all 59 Starlight Tactics achievements.
Complete Combat Fleet Training
Complete the entire USF and NAN Campaign
Complete the USF Campaign as a Lieutenant
Complete the USF Campaign as a Captain
Complete the USF Campaign as an Admiral
Complete the NAN Campaign as a Subcommander
Complete the NAN Campaign as a Commander
Complete the NAN Campaign as a Supreme Commander
Achieve victory in first Campaign mission
Achieve victory in 10 Campaign missions
Achieve victory in 20 Campaign missions
Achieve victory in 40 Campaign missions
Complete first skirmish mission
Complete 10 skirmish missions
Complete 100 skirmish missions
Complete 1000 skirmish missions
Fire first plasma salvo
Fire 10 plasma salvos
Fire 100 plasma salvos
Fire 500 plasma salvos
Fill all the slips in the USF SpaceDock
Fill all the slips in the NAN SpaceDock
Own one of each type of USF ship
Own one of each type of NAN ship
Own the USF Alamo
Own the USF Alamo and USF San Jacinto
Own the USF Los Angeles and USF San Francisco
Own the USF Ronald Reagan and USF Mikhael Gorbachev
Own the NAN Ares
Own the NAN Leonidas and NAN Sparta
Own the NAN Libya, NAN Somalia, and NAN Sahara
Own the NAN Guleed Samakab
Own five USF Destroyers
Own five USF Stealth Ships
Own five USF LCS'
Own five USF Cruisers
Own five USF Carriers
Own five NAN Frigates and five NAN Corvettes
Own five NAN Battleships
Own five NAN Cruisers
Own five of each type of NAN Carrier
Neutralize first target in Campaign
Neutralize 20 enemy vessels in Campaign
Neutralize 50 enemy vessels in Campaign
Neutralize 100 enemy vessels in Campaign
Own the Earth Fleet from Starlight Inception (Colin Powell, Alamo, Sun Tzu, Philadelphia, Midway, Independence)
Neutralize an enemy vessel by ramming it
Neutralize a friendly ship by ramming it
Neutralize an enemy ship using self destruction
Neutralize an enemy ship with a drone
Expose an enemy stealthed ship using EMP
Face the NAN Olympus Frigate in Campaign
Face the NAN Tao Cruiser in Campaign
Face the NAN New Saharan Batteship in Campaign
Face the NAN Houssam Carrier in Campaign
Complete the last USF mission with just the USF Independence
Complete the last NAN mission with just the NAN Xerxes
Complete the USF Campaign without ever losing a ship
Complete the NAN Campaign without ever losing a ship