Here is the full list of all 45 Croixleur Sigma achievements.
Defeat 4,000 monsters.
Collect all Weapons with Francesca.
Collect all the Weapons.
Defeat 1,000 monsters with mid-air attacks.
Collect 10,000 coins.
Absorb 25 enemy attacks using in-dash invincibility.
Build a Chain of over 250.
Clear 10 Challenges in Challenge Mode.
Defeat 400 monsters with mid-air attacks.
Collect all Weapons with Lucrezia.
Collect 4,000 coins.
Defeat 1,000 monsters.
Clear Story Mode. Now if you do it a bit quicker...?
Build a Chain of over 100.
Collect a Weapon.
Defeat 100 monsters with mid-air attacks.
Collect 1,000 coins.
Survive to the end of Score Attack Mode.
Defeat 100 monsters.
Clear 1 Challenge in Challenge Mode.
Collect 100 coins.
Clear Lucrezia's story, using no continues and reaching the final stage in less than 10 mins.
Clear Francesca's story, using no continues and reaching the final stage in less than 10 mins.
Clear Bonus Mode.
Clear 20 Challenges in Challenge Mode.
Clear 30 Challenges in Challenge Mode.
Defeat 10,000 monsters.
Clear Story Mode or Arcade Mode with Lucrezia and without using Invincible Attacks.
Clear Story Mode or Arcade Mode with Francesca and without using Invincible Attacks.
Clear Bonus Mode without using Invincible Attacks.
Build a Chain of over 400.
Absorb 100 enemy attacks using in-dash invincibility.
Defeat 100 monsters in Survival Mode without taking damage.
Defeat 250 monsters in Survival Mode without taking damage.
Clear Story Mode or Arcade Mode with Lucrezia and achieve the #1 rank.
Clear Story Mode or Arcade Mode with Francesca and achieve the #1 rank.
Achieve the #1 rank in Bonus Mode.
Achieve the #1 rank in Score Attack Mode.
Achieve the #1 rank in Survival Mode.
Achieve the #1 rank in all modes.
Beat Story Mode or Arcade Mode with Francesca and without using Invincible Attacks.
Beat Story Mode or Arcade Mode with Lucrezia and without using Invincible Attacks.
Defeat Francesca in Score Attack Mode.
Defeat Lucrezia in Score Attack Mode.
Unlock all achievements. Obtain this to be a true Croixleur Master!