Demo is pretty limited compared to the full-game, but we can actually get access to most of the game through some glitches. But:

• The finger upgrade on the Rain Bridge level (considered finger 3) is inaccessible inside of an impenetrable block.
• Plains is fully cut off after entering
• Memorandum has a blocking wall before the three finger door towards Heaven
• Purgatory has a blocking wall towards Ice Lands.
• Blocking wall in Fountains area, but you can jump off the side and spawn ahead of it, making your way to Black Fountain

But with some glitches we can make make it to Darkness and Crimson River, so we can get a total of 4 finger upgrades.

if speedrunning the demo version for Black Fountain, you can still do it, but afaik there's no ingame speedrun timer, so we need to figure out what to do regarding that.