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:
Graveyard
18:06
Windmill:
25:06
Stone pillar
32:35
East Arena
38.34
Waterfall (slight detour to save when first arriving)
56:35
Waterfall (on the way back after water wheel jumps)
1:02:37
Water Tower
1:08:22
West Idol Stairs
1:16:01
Main Gate (final save after arriving and seeing the first cut scene)
1:26:15
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.