Here is the full list of all 41 Cataegis : The White Wind achievements.
Destroy a flier on water electrocuted
Get your first death
Slash a missile
Slash a thrown spear
Juggle the White Drone until it explodes
Find the breakable wall in the Main Stage
Clear the Main Stage
Get the two guards to enter your cell in the Ziggurat Prison
Draw in and survive the wave of Ziggurat patrollers in the Ziggurat Prison
Provoke no fights when in the Ziggurat Prison
Destroy the turret in the Prison Halls before the Alpha gets to it
Kill the Necromancer in the Ziggurat
Spare the Necromancer in the Ziggurat
Kill the Gorgon in the Ziggurat
Spare the Gorgon in the Ziggurat
Survive the Dungeon's first floor in the Trap Room when you're dropped
Kill the Dryad in the Ziggurat
Spare the Dryad in the Ziggurat
Don't let the Low Levels jam the elevator gears in the Ziggurat
Kill the Insect in the Ziggurat
Spare the Insect in the Ziggurat
Clear the Ziggurat mode killing no bosses
Clear the Ziggurat mode killing all bosses
Destroy the Death Dampener machine
Drop all existing Flier Drones on the water in the Main Stage
Get an ending where you escape from the Ziggurat
Free the survivors from the Ziggurat in your ending
Be granted freedom alone from the Ziggurat in your ending
Make it to Ishtar's throne room
Kill the Necromancer's support corpse
Acquire the Necromancer's Pendant
Acquire Gorgon's Blood
Acquire Alruna's Seed
Acquire the Biotech Boost
Collect all Data Files
Collect all BGM Files
Destroy the merged Kazazak and Alpha
Tell Euryale to go away
Get the best affinity with Euryale
Assault Shiah when she asks you to kneel
Beat a Ziggurat boss without losing a life