I’ve just tried it on an alternative account for which I had no mastery in Bangkok and it definitely worked for me, but it seems that, as you’ve reported, if it doesn’t unlock when it is supposed to unlock, then it never unlocks at all. Just in case you’d missed something, here’s the video of me doing it. Keep in mind that the Xbox DVR doesn’t allow you to record system notifications, so you won’t see where the achievement actually popped, but I’ll explain when it happened below.
Having shot all 18 elephants I ran downstairs to trigger the tears of blood from the elephants Easter egg and the “I Will Cry if I Want To” challenge unlocked as I entered the atrium. When I went outside the elephants were crying tears of blood, so I pulled out my pistol and allowed myself to get killed. I reloaded an auto-save just at the point where I pulled out the pistol, but no achievement popped. I allowed myself to get killed again and just as it went to the Replay menu the achievement popped.
Remember, you must either complete the mission or die and reload at auto-saves after completing the challenge for it to unlock.