This achievement is story-related and cannot be missed.
*** Spoiler - click to reveal ***Some more time will pass from the previous achievement. When Clementine is sequestered in a shed, she can grab thread from the nearby bench. She needs to pull up a table attached to the shed's wall. She ascends the table and grabs a hammer on top of a shelf. She climbs back down and pries open a board nailed to the corner wall. Clementine approaches the cabin, walking past the front door to the side of the house. She can crawl under the house from here by prying open the trim.
After crawling under the house, she sees a loose board that she can cut open with her knife. She breaches into the house and climbs upstairs and into the bathroom, where she finds a needle above the sink. Clementine hears a person heading upstairs and hides into the bathroom's linen closet. Afterward, she leaves and enters the bedroom door opposite the bathroom. She meets a young girl and can choose whether or not to promise being friends. After doing a pinky swear, Clementine will receive hydrogen peroxide. She leaves and heads to the last bedroom upstairs, where a bandage substitute is found on a desk. When all is found, the "Sneaky" achievement unlocks.
EDIT - Thank you to drabik for clarifying the location of the thread and needle. Also, thank you to SDREW44 and TheIcemanCometh for clarifying the location of the hydrogen peroxide. I have not done a playthrough to analyze how this is obtained if a pinky swear is refused.