This is a missable achievement.
The description of the achievement is vague, but it actually requires a newspaper that previously criticised Poirot to praise him eventually. To do so, you'd need to prevent the 4th murder, and ensure that no manner of harm will befall to the potential 4th victim, Donbar (owner of the Black Swan Hotel).
After deducing that Donbar is the 4th victim from the burned records, choose to call him yourself instead of letting Japp do so. When speaking to Donbar, you must ensure that he doesn't get a heart attack.
The options are: speak to Donbar, ask if he has heard about the investigations, Cust is a suspect, and keep watch.
Continue with the game until the final time you're in your apartment. Before deciding on whether to load the gun with real bullets or blanks, go to the usual round table beside the sofa, and read the last newspaper. As long as Donbar doesn't suffer a heart attack, the papers will praise Poirot, and the achievement will unlock.
As such, if you've deliberately caused Donbar to suffer a heart attack to make a mistake towards the "Large Donkey" achievement, you'd need to replay the game from scratch to unlock this achievement.