Here is the full list of all 13 Katana Kata achievements.
Meet your death for the first time
Kill your first bathing bandit
Kill your first karate warrior
Kill your first sumo warrior
Kill your first bandit
Kill your first samurai
Kill your first armored samurai
Kill your first ninja
Kill your first monk
Kill your first master
Break your weapon for the first time
Find and collect six types of weapons
Reach maximum level