These Achievements (called Trophies in-game) can be viewed by talking to the Trophy collector (Nether Noble) in the middle of the Data collector (Fairy) and the Memories collector (Mothman).

Achievement	How to unlock
A Taste of Curry to Come	Clear Ep. 4: Yellow, Rabbit, and Curry.
Bloodis' Big Secret	Clear Ep. 6: The Sixth Warrior.
Fight in the Frozen Wasteland	Clear Ep. 5: The One Who Controls Death.
Founding an Army	Clear Ep. 2: Demon General.
Some Kind of Gale	Clear Ep. 3: His Name is Zeroken.
The First Alliance	Clear Ep. 1: Prelude to Vengeance.
Vengeance Complete	Obtain all other trophies.