This does not fulfill the requirements at all.

I think the problem could be defined a bit more thoroughly.

What about strings which contain both dashes and underscores, like 'the_well-known_guy'? Even though we can safely guess that the result should be 'theWell-knownGuy', finding a consistent algorithm would be quite difficult. What about strings with a leading underscore? More importantly, what about strings which contain uppercase characters? The sample tests seem to indicate that uppercase letters in the input should be preserved, yet I managed to pass all the tests with a solution which doesn't. For example, that solution would fail on the string 'the_UK_guy', returning 'theUkGuy'.

Do note that I'm not suggesting the Kata be made more difficult, just better defined, no matter if the definition is arbitrary. As it stands, I think it's just encouraging people not to try to learn more about a problem, which is a terrible habit.

You're right, I'm quite surprised that I didn't check for that optimization. I haven't written Haskell in a while, but I know that at the time I loved to fiddle with things and look at the Core, to see what improvements could be made. I guess now I have no choice but to get back into it ;)

[toUpper c] ++ (replicate i $ toLower c) is just toUpper c : replicate i $ toLower c. As the other commenter noted, there are some unecessary statements.

This probably accumulates a bunch of costly thunks.

Using list index is a bad idea! Also, many of the guards here should be replaced with case expressions or if/else.

Danger: Heavy use of (!!), errors, and list append is rarely a good idea.

This is definitely overcomplicated, my main goal here was to learn and practice creating larger/more complex programs.

I'm not sure that using the reverse function application operator (&) is a good idea.

"Best practices" should really include a function signature.
The function used to compare directions is also not extensible and would never be used except inside of dirReduce. It should probably be included in a where clause or modified.

Using nub might be a bad idea, see https://www.reddit.com/r/haskellquestions/comments/7f83jl/nub_sort_or_sort_nub/

Improved version of the current top answer.