All existing answers seem to be preoccupied with the idea that it makes a difference how many "percentages" and "populations" are being referenced, but that's not really the issue. Because "percentage of the population living in urban areas" is a somewhat long and unwieldy noun phrase, let's substitute something simpler - number of people:
1: The chart shows the number of people in the world and in different continents.
But the basic phrasing there is clumsy, so let's make some minimal changes to clarify things...
2: The chart shows the total number of people in the whole world, and in each different continent.
The same logical arguments apply to singular/plural number in my example as OP's percentage, but at least now it's easier to see that the singular version can be understood to involve elision/deletion...
3: The chart shows the total number of people in the whole world, and the number of people in each different continent. (the "fully expanded" version of #2 above)
Although it's effectively a stylistic choice whether to pluralize number in #2, I personally would almost always go for the singular in contexts like that. Consider an even simpler case...
This chart shows the price of electricity in Britain and other OECD countries.
Pragmatically, we're not likely to be looking at a chart with only one (average?) price, but I suggest no competent writer would be likely to pluralize prices there.
TL;DR: There's no actual need to pluralize percentage or population in OP's context. Grammatically speaking you could, but stylistically that would be a bad choice for both nouns.