All the achievements are secret, but they are all relatively simple. Get the majority of the achievements by unlocking new officers (just complete mission targets on Easy or Normal) and by completing the Musou mode with each officer (on any difficulty).

Additionally, there are achievements for completing all the mission targets and clearing all the stages (the latter probably pops up before the former).

Clear Musou mode with all the available officers (solo or co-op doesn't matter, but all the officers available in Musou mode need to clear it). Additionally, all officers need to attain level 50 (which effectively maxxes out their skill tree).

Lastly, clear all stages (not targets) on Chaos difficulty. Yeah, good luck with this one!