I did this on my NG+ run, which is started upon continuing from the final save in your NG run.
I followed along (mostly) with this speedrun. Sorry about the crappy quality- it didn't look nearly as bad on my phone as it does on my PC:
I mirrored the run fairly closely, but there were a few parts that I couldn't replicate, even with nearby saves and multiple tries, so I had to improvise in a few places.
If you want to be able to watch in higher quality, this run seems similar:
Here are my save times/locations as I progressed:
Waterfall (slight detour to save when first arriving)
Waterfall (on the way back after water wheel jumps)
West Idol Stairs
Main Gate (final save after arriving and seeing the first cut scene)
I don't know my final time as the game doesn't create a save after completing NG+, but I had enough time from the final save to beat the game AND get the Watermelon ending, which added a minute or two to the final trek down the beach.