To obtain this achievement you must kill all the enemies in one level. If you just started killing enemies on the first level I recommend killing all the enemies throughout the game so you can obtain the God of Death achievement which is for killing all the enemies in each level. If you decide to go for not killing a single enemy run of the game there is chapter select so you can obtain the Oni medal (killing all enemies medal) after beating the game for the first time or beating a chapter.
*I recently wrote a guide for getting the first non killing medal you can check that out for some additional hints mainly with the two big hints regarding the last level where you get all the medals regardless and difficulties settings for the game