How to Acquire
Complete The Brigmore Witches without killing anyone. This can be achieved by utilizing Daud's non-lethal equipment, which includes sleep darts and stun mines. Choking, and especially the Strong Arms Bone Charm, are extremely effective, as is applying a generally stealthier approach to missions, including finding alternative routes to minimize the number of enemies and the chance of detection.
If Daud chokes out Edgar Wakefield in The Dead Eels and leaves him on the Undine, he will, on his return, find that Lizzy Stride has killed Wakefield. This will not count against Cleanest Hands. However, turning off Mortimer Hat's life support in that same mission does count as a kill.