Here is the full list of all 32 Exception achievements.
Fully upgrade all special attacks
100% the entire game
Collect every byte
Finish 64 levels while destroying every enemy
Destroy 75 enemies with down dash attack
Destroy 50 enemies with up dash attack
Destroy 100 turret enemies
Finish 32 levels without destroying an enemy
Destroy 100 enemies with sword throw attack
Down dash four enemies in one jump
Up dash four enemies in one jump
Earn a style bonus
Earn an air combo bonus
Complete the game
Fully upgrade a special attack
Finish a level with four bonuses
Defeat the monster in world twelve
Run five kilometers
Achieve a 4-star rating on 64 levels
Destroy the boss in world eight
Destroy 200 flying enemies
Jump 2000 times
Upgrade a special attack
Destroy 150 ground enemies
Achieve a 4-star rating on 32 levels
Escape the monster in world four
Unlock all special attacks
Complete a level without using all transitions
Collect a byte
Destroy the player
Finish a level with three bonuses
Finish the first level