Are the requirements for the Treasure Raider achievement limited to one save/playthrough?

Solution 1:

According to this guide:

They can be collected cumulatively through all playthroughs...

I also found that the author of the guide had the same problem, albeit on another level:

If you die after getting a phial and load to the last save point, it’ll still register that phial. Unless you make it to a further save point before shutting off your 360 though, you’ll lose the record of that phial and have to get it next time you play. I missed one on the second level due to this, so just be wary!