This achievement can be obtained very easily on the first level. A level consists of entering one of the doors in the forest, returning to the same set of door entrances. This is not for the prolouge.
Even on the hardest difficulty, you can get away with only using your arrows. If you hold
in the direction of the enemies you will spam arrows.
It is best to save your coins to upgrade the fire arrows if you are attempting this in your first run. Remember, you can always replay the first mission immediately after completing it but returning to the first door.
Just DO NOTPRESS at any time during the level and you will be fine. Even if you hit a wall or a door, it still screws the acheivement.