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