For anyone trying to complete this achievement using the Offline mode/cloud save.
I found all other tips to be vague when trying to attempt this on my own so I figured I would list what worked for me. I decided, after many failed attempts at getting the offline/cloud method to work, to treat it like it was a steam game. On steam the save files sync immediately after you completely exit the game.
1) Start fresh: delete all local and online cloud saves
2) Launch the game while connected to the internet and start a new game
3) Personally I completed the first level while connected to the internet before deciding to use the offline method. So complete the first level and wait until the beginning of the second level loads up.
4) Once the second level loads up immediately pause and exit to main menu
5) Close the game using the "Quit" function (this completely kills the application
6) Now since you were playing the game online throughout the first level the local save file will start you at the beginning of level 2.
7) Before doing anything else go to your settings and disconnect from the internet.
8) Re-launch Little Nightmares (in offline mode) and select to resume game
9) *****If you happen to die while attempting level 2 immediately "Quit" out of your game session (no need to go to the main menu) and go to your local save files and delete the save game information. It is important to note that sometimes you may have to delete it twice before it is completely cleared. Before re-launching Little Nightmares connect your console to the internet. When you relaunch the game it will sync the save that was uploaded to the cloud and you can continue from there with zero deaths.
10) Use this method after every level to create a backup save.
-Pausing will not add to in game time
-Restarting a checkpoint before the death registers will not count as a death
-If you want to be connected to the internet when the game pops your achievement I would suggest waiting until you've completely killed the geisha. Once the geisha is dead just pause the game, connect to the internet and finish the ending. (This is the method I used and it worked)
-The achievement will not pop until you start ascending the stairs after killing the geisha and walking through the Gluttons with your newly acquired power.
Final Note: The tips above are my notes on what worked for me after reading many different strategies and trying multiple different methods.