The Stay True to Yourself achievement is unlocked on the Silent But Dadly level
Playing the game on easy difficulty will make this achievement really easy as you can just walk in front of the scientists without having to actually sneak to the cafeteria. Once you reach the cafeteria window and climb through, the achievement will unlock.
You can unlock this achievement and the Everybody Loves Joe achievement in one playthrough without having to play the entire level again with a checkpoint reload at the very last second at the end of the chapter.
To be safe, I would choose to go to the cafeteria without the disguise first because I don't know if this method works the other way around.