> I've been able to do get past this to the third floor via mana mushrooms, but everytime I try to tackle this puzzle I can't make heads nor tails of the riddle, or even how to cross the chasm. I know that at a certain point in the tower I get "refreshed" with the right timing, but that's all I've been able to figure out.
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The first part of the riddle refers to how long (counted in turns) the sands run through the black/white hourglasses. You might have noticed already that the black doors can be passed through only when the black sands are still falling. [One exception to the turns count is when you get zapped by the laser beams, upon which you lose two extra turns in addition to the move.]

The "height" of the second part refers not to the chasm but an even greater height which can be gazed upon. And the "last gasp of strength" is of course right when you're about to collapse.

Solving the main puzzle to access the pedestal involves getting through a certain door - you'll need the Atlas Cap and Buff Bandanna to have enough stamina. Once you have both items, you'll have to flip both hourglasses on a run-through, one of them twice.

Before that, to get the Atlas Cap you'll only need to get to the north side of the chasm quickly enough. You can't cross the chasm directly, but there's a roundabout way to get there. Only one hourglass flip is needed for this step.