How "well regulated" must the input voltage to a DC-DC boost controller be?
Ok, so the regulator will have it's own bandwidth, probably not higher than few kiloherz. Obviously you will want any fluctuations of the input to be lower than that. But more accurate answer requires some specifics: power, current, input/output voltage, load properties.

But the bottom line actually should be "relax, just do it". A chance to screw up if you work according to the application notes is very low.

Pay attention! Your input will be DC, nothing to do with mains!!!