Here is the full list of all 20 Valkyria Chronicles achievements. It takes around 50-60 hours to unlock all of the achievements on Windows.
Kill 1000 enemy units
Train all character classes to level 20
Learn every order
Commission all tank upgrades (including all three level 3 Edelweiss upgrades) and collect all enemy ace tank parts
Complete all chapters and reports
Beat the game and begin a new game from the saved file
Kill 500 enemy units
Complete the second Chapter 15 battle "To Fell a Citadel"
Complete the Chapter 14 battle "Showdown at Naggiar"
Complete the Chapter 10 battle "Liberation of Fouzen"
Kill 250 enemy units
Complete any chapter battle after Chapter 10 without any of your units being reduced to 0 HP
Earn an A Rank on any chapter battle after Chapter 10
Complete the Chapter 9 battle "Kidnapping of Cordelia"
Kill an enemy ace
Have a soldier who has fallen in combat survive either by calling a medic or clearing the battle before they die
Let a character who has unlocked his/her hidden potential die in combat
Unlock the full personnel profiles for all recruits
Commission all weapon upgrades and collect all enemy ace and royal weapons
Earn an A Rank on every battle, including all reports and all ranks of all skirmish battles