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