The easiest way to be assured of obtaining this achievement is to trigger the 'Level 3 Classified' Ending.
To do so, the player must take the following actions in one play through (Story Mode):
*** Spoiler - click to reveal ***
1) In the chapter 'Intrusion' while playing as Conrad you need to ensure that he does not escape in the speedboat. Do this by either:
a) Ensure that he dies during his attempt to escape the Duke of Milan. When Olsen points his gun at you, fail the QTE. Conrad will be shot and bleed to death at sea, taking no further part in the story.
or;
b) Ensure that he stays on the Duke of Milan, and is therefore with the others on the Ourang Medan
2) In the chapter 'Danny' while playing as Fliss, you will reach a short cutscene where a jumpy Danny confuses a hat on some bags as a person, and knocks the hat to the floor. When the player regains control, have Fliss pick up the hat for Secret #41 - Medan hat.
This reveals that the name of the ship ends with 'G MEDAN'.
3) In the chapter 'Distress Signal' while playing as Alex, you will reach a point where Fliss will boost you up from the weather deck of the ship to the upper levels. After forcing a door, you will enter the bridge. Turn immediately to the left, to find 'Secret #42 - Ships Logbook' on a desk. Flip the page to reveal that the name of the ship begins with 'OURANG M'.
4) Later in 'Distress Signal', Alex will discover a working radio. When given the option to speak, choose 'Instructive', followed by 'Anxious' to communicate the ship's coordinates.
5) Towards the end of 'Distress Signal', ensure that Alex remains at the radio by sending Brad, (Choose 'Encouraging' when prompted in the dialogue) and either Fliss or Julia down the hole.
6) In the chapter 'Depths', while playing as Brad. Find the generator in the engine room. (It looks like a switchboard, with lots of holes and three switches. Walk close enough to it and you will trigger a cut scene). When prompted, throw the switch.
The radio springs back to life, and Alex will reveal the name of the ship to the military.
(This also unlocks the achievement 'The name of this vessel')
7) The final step requires that anyone left alive is stranded on the Ourang Medan. To do so, means that the distributor cap must be destroyed. In the chapter 'Matters of the Heart' while playing as Alex, you will find Olsen in the kitchen, covered in rats with the distributor cap resting on his chest. Grab the distributor cap, and fail any of the 3 QTEs.
A rat will bite Alex, causing him to drop the distributor cap down the elevator shaft, where it is destroyed by the falling elevator.
With the Duke of Milan inoperable, and no other hope of escape, any of the remaining survivors of your playthrough will now be trapped on the Ourang Medan. They will gather on the weather deck, to await their fate before the credits roll. In a post-credits scene, the military arrives by helicopter. Knowing the identify of the ship and what it carries, they execute all of the survivors in order to keep the secrets of the Oraung Medan.
The achievement will then unlock.