Most importantly, while teamed, incapacitation does not count as a death (from what I remember).
There's really not much to this achievement. Just take your time and carefully clear the objectives (while staying together if in a team).
The easiest mission to complete this on would be a mission that has no chances of instant death. Ammunition, The River, and Walton's Gold; while these missions are usually more straight-forward, they do have an increased chance of instant death. Cannon fire in Ammunition will likely kill instantly; incapacitation while on the boat in The River will leave you completely dead; dynamite could also claim a life in Walton's Gold.
Sticking to Escape, Kidnapped Girl, and The Herd will increase your chances of completing this achievement.