So after watching Sylvie's 2-item 100% challenge run, I decided to try a similar 1-item challenge run to see what the limits would be.
My initial expectations were low, so colour me surprised that I eventually managed to get all the way up to 91% completion!
(Note: The finale isn't completable within the rules of the challenge, so I did have to cheat a little to get my percentage score)
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Here's the exact list of collectibles I wasn't able to get, as denoted in the checklist posted on Steam (Warning: Item location spoilers, of course):
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Gems:
Valley - Flooded Chamber
Underwater - Pot/Aquarium
Underwater - Shrink Cave Under Catfish w/ Octo
Castle - Moat Shrink Tunnel
Sewer - Caged Gem Wand/Switch Puzzle
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Ores:
Caves - Bomb Secret
Hymnir - Floating Platform From Below
Hymnir - Bomb Over Lava Secret
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Keys:
Sewers - Falling Pillar
??? - Above Crusher
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Chests:
Valley - Great Tree Top
Sewer - Shrink Secret Room
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Other:
Upgraded Book
Duke