What is the order of dragon difficulty?

I think it is best to cite this wiki page here. The common dragon types are:

  • Dragon: Brown-colored dragons; they are the first dragons encountered in Skyrim and are the weakest.
  • Blood Dragon: Green-colored dragons that have finned crowns and spade-like tails.
  • Frost Dragon: White and blue, ice-affiliated dragons with black-colored dorsal spines.
  • Elder Dragon: Bronze-scaled dragons with arrow-shaped tails; second to Ancient Dragons.
  • Ancient Dragon: Red, black and orange-colored dragons; The most powerful dragon in the base game.
  • Revered Dragon: Orange-colored dragons introduced in Dawnguard; second most powerful variant.
  • Legendary Dragon: Black, purple-colored. Maximum level dragon introduced in Dawnguard; most powerful variant.

There are a couple of other dragons inside the game. Other than some skeletal dragons, that do not drop scales nor yield a soul; their names are Dumehviir the undead dragon, two red dragons Nafaalilargus and Odahviing and the black dragon Alduin. You can look for specifics on them at the wiki pages.