According to the Fandom (dot-com) Wiki for Inscryption you can achieve this via the following:
If the Captive File dies during the fight with The Archivist, a text file will be created in the same directory as the file, asking the player to delete it themselves to respect the rules of the game. This achievement is earned by deleting the file or by simply moving it to a different location.
Based on this you will have to make sure you destroy one of the Captive File creature cards during that boss fight. Remember that these cards are created using actual files from your computer, so note which file you choose during the prompt. Once the card is defeated go to that file on your actual computer and move it to a different folder, or delete it if you don't care (you can restore it from your recycle bin if you "Don't empty it" as per the description of the achievement.