It's no harder, it just punishes impatience more. The player's footing on certain bridges / ledges / paths sometimes caused death, but the same basic cautious principles used in later Souls games are all represented in Demon's.
Quick EDIT: you can also chip away at each of the five arch-stones at your own pace, kinda like picking your play order of Mega Man levels. Certain things from certain levels really help certain things in other levels (ambiguous, I know). Don't play each level to its conclusion. Try to beat (example) 1-1, then 3-1, then 2-1, then maybe 2-2, then 4-1, then maybe 1-2, etc.