Here is the full list of all 41 Blade Prince Academy achievements.
Finish the Tutorial
Obtain Gadhoo
Obtain Vekkio
Obtain Orchid
Obtain M'aki
Obtain Themios
Obtain Diamante
Obtain Anatonio
Obtain Zenesh
Defeat Acid Hair
Defeat King Mago
Defeat the Abomination
Defeat Poison
Defeat the Black Mages
Defeat Zian Torrus
Defeat Ethyllion
Defeat the Vampire Queen
Enchant a Pact to Level 1
Enchant a Pact to Level 2
Enchant a Pact to Level 3
Upgrade the Laboratory to the maximum
Upgrade the Infirmary to the maximum
Upgrade the Altar to the maximum
Complete 10 missions with a Threat Level increased by 7
Participate to a Party
Participate to a max level Party
Win the Mega Jackpot in a Casino
Have a level 6 Pact or higher
Phoebos reach level 10
O'Ren reach level 10
Selena reach level 10
Gadhoo reach level 10
Vekkio reach level 10
Orchid reach level 10
M'aki reach level 10
Themios reach level 10
Diamante reach level 10
Anatonio reach level 10
Zenesh reach level 10
Kill an ally by accident
Perfom 3 combos in 5 seconds