This achievement is obtained on Operation D Mission 1.
You cannot use anything except the Bruteshot, melee, and grenades to throughout the mission. You don't come with a Bruteshot so you will need to kill a brute for one. They are the enemies with the jetpacks. Their are many grenade boxes all over which makes the achievement much easier. The whole mission is to destroy two doors and go into the last one to complete the mission. You do not have to kill anybody at all if you chose not to.
This was recorded on the Xbox One but the achievement is completed in the exact same way.