After completing all the Legend and Dream modes this was the last achievement I had left to score. You can check to see how many of each kill type you have in the Gallery. I had about 1900 Ujoken kills after finishing both of Toki's modes. (Toki being the only character who naturally uses Ujoken).
To boost quickly, I leveled Toki by replaying his Dream Mode level 2. Using his X, X, X, Y combo I was able to score about 500 kills in about 25 minutes.
This can be increased by equipping the "Ujoken Wisdom" skill, which is directly at the top of Toki's Meridian Chart. It's up two, and one to the left of the northern Training Plateau.
Also: other characters can equip and utilize this skill. However, I've found that it's quicker to level Toki since you're scoring needed kills while working towards the Ujoken Wisdom skill.