To unlock the Surgical Sniper trophy in Assassin's Creed Odyssey, you must first purchase the third episode of Legacy of the First Blade (or own the Season Pass) and download Episode 3.
You will get the Golden Harbinger after killing Gergis the Herald during the Smoke and Fury storyline quest. Equip it as one of your melee weapons. You can then use a bow to get the headshots -- you don't need to attempt to get headshot kills with the Golden Harbinger and you don't even need to have low health when you go for this trophy.
The easiest way to do this is to either headshot kill animals or civilians, although you can, of course, headshot enemies as well.