This achievement takes a bit of skill and can be a bit frustrating while being insanely easy... You have to "steal" a post card from the gift shop right at the beginning of your trip into the cave. (and get the following achievement...)
Then you will have to transport this postcard over your whole journey in the cave to return it right at the end! This is not too hard, just a little frustrating because of the item swapping you'll have to do. Remember to always take the card with you! And at the end stand by the postcards with your character holding the card and press
X. Voilà. Achievement unlocked.
Note: Thanks to
https://www.trueachievements.com/OniKawazu.htm for reminding: When coming to the hunter puzzle - the front character (getting "eaten" by the monster) will lose the postcard (if he was the one carrying it)! Give the postcard to your second or third character (Reminder: The hunter puzzle is just the one after the puzzle of the twins. Even if you don't have them with you, you will pass that "scary" house (with that barking dog) and then get to the hunter puzzle. So that's the moment you have to be careful with your postcard!)