This is a story related achievement which will unlock with natural story progression.
Once you have progressed in the story and found out about the stolen cane, talk to the doctor at the clinic. He will mention the cane and give you access to cabinet at the back of the clinic. Once you open the cabinet you will find yourself looking at various parts of other canes.
Your task is now to build the cane described by the artist Sickert.
An ebony cane, 35 inches long with a detailed silver knob. The cane also has a silver band and silver detailed base.
Third cane from the left (Black Cane)
Fourth knob from the left (Silver detailed knob)
Eighth silver ringlet (Far right)
Fourth silver base (Also detailed with the same design as the knob)