The first seven worlds... nothing too terrible in terms of difficulty.
The difficulty skyrockets in world 8. Basically that's where the real game begins.
8-2 without a weapon is pure hell. That one level took me many hours to learn. 8-3 is supposed to be the hardest level, but only the infamous final section with the dropping platforms and the bats is that difficult. 8-4 without a weapon is grueling but I managed to do it.
I'm not sure which is tougher, Adventure Island or Battletoads. I feel like I've never beaten a tougher game than this even though I used many continues.
This is what Adventure Island 8-2 and 8-4 looks like if you happen to die and lose your weapon. The amount of memorization required is insane.
Someday I'd like to 1cc Adventure Island, but I'm not even close to being able to do that now.