This is one of two achievements in the title update that doesn't unlock upon loading up an older save. Prior to making a new game: I would recommend loading up your old save (if applicable) to unlock the 3 achievements below:
Then start a new game (or begin a new game if this is your first playthrough) and ensure that you kill the first 5 enemies that you come across to earn the achievement below:
From there, just go through the level as you normally would. You can skip all the enemies by hopping past them or fight them if you want. Regardless, the achievement will pop after you finish traversing the first level.