Here is the full list of all 21 Kingdom of Blades achievements.
Reinforcements have arrived
Become a bad ass ninja
Become a bad ass ninja (but fail)
Experience your own mortality
Make it snow
They'll never get past your metal plate!
Just a good ol' regular slicing
Ok now that's quite a lot of dead bodies
All shall submit and kneel before you!
Bathe in the blood of your enemies
Wield the power of the gods
You never saw them coming
Face the anger of the gods
The worst way to go...
Death by pretty stones
Complete Chapter One
Complete Chapter Two
Complete Chapter Three
Complete Chapter Four
Defeat the first boss in Endless Mode
Defeat the tenth boss in Endless Mode