Some notes on things that won't nullify this achievement:
- Wearing reflective damaging armour like Assassins does not negate it (in my experience it doesn't actually reflect without a weapon anyway)
- Gaining armour or weapon proficiency does not negate it
- Offhands, fishing rods, or instruments (even ones with Force) do not negate it
- Force based brews/vials do not negate it
- A spell like Flaring Crescent, despite technically putting a weapon in your hand slot, does not negate it, nor does killing something with it