From second to last paragraph above: "The Trophy/Achievement may be glitched and despite having all 107 rings in your inventory it may not register. In this case drop 15 rings, then pick them up again, then drop a different 15 and pick them up. Do this until it registers. DO NOT drop any more than 15 to be safe. The game only allows about 30 rings to be on the ground at any time and will delete any number more than that. It's recommended that you make a backup of your save before doing this. It is still possible to obtain all of the rings in a later runthrough as each has a specific location, so don't worry if you didnt get the NG+ rings in NG+. (Obtained every ring at NG+5, confirmed)."