(Haven't played Mountains of Madness yet)

So most mysteries have a baseline difficulty. They're either:

1. Get 1 clue per player.

2. Get 1/2 clue per player and do some moderate task (close a gate, etc.)

3. Zero clues and do a difficulty task (defeat an epic monster, etc.)

With that in mind, my toughest mysteries award goes to:

Runner up: Hunting the thousand

Defeat a number of monsters (moderate task) AND spend 1 clue per player bare minimum (if you only defeat 4 toughness monsters). More often it will end up being 2 clues per player. You have to hunt down the clues, then hunt down the monsters, and the investigators good at getting clues are more often than not the weakest ones at fighting monsters so you'll have to spend more time transferring those clues to the monster killers. This mystery is basically twice as difficult or more than average and easily makes Shub twice as hard overall if it comes up.

Winner: Voice of Azathoth

Get 1 clue per player AND acquire an artifact (difficult task). Getting an artifact is probably the single most difficult task in the game. The only reliable way is doing expeditions, which are pretty tough. Spend several turns traveling to the out of the way location, then take what's probably a less than 50/50 shot at successfully completing the expedition. Fail, and spend several more turns trekking to the next expedition. Worse, a number of expeditions don't grant an artifact even if you succeed!

Then on top of that, not only do you have to spend 1 clue per player, but all those clues have to be in the possession of a single player.

Either half (clues, artifact) would be plenty for a single mystery. Voice of Azathoth combines both. We have yet to not lose a game where this mystery comes up. We're at the verge of house ruling it so that you only need the artifact and not the clues. Another debated house ruling is to count it as 2 mysteries when solved. It's THAT hard!

I do not have a tough time getting artifacts, but it more of the timing of the mysteries that make them difficult.

Last night we had a mystery of having to kill wendigos and spend 2 clues, but our asset deck refused to give us weapons and we got two horrid rumors, one that eats mythos deck and another that does dmg if you do not kill the epic quick enough. We only had Lilly as our main enforcer while others were support. And if we did not focus as well on our turn, hypothermia claims us all. We were able to finish mystery but late in the game due to having to handle rumors, we would have won if the one rumor did not go off twice before we got to it. Mystery was north side of board while dangerous rumor was far south, so we lose that travel time as well.

The Serpent Crown Mystery is certainly harder than the Voice of Azathoth: gain the Crown, spend the same number of clues, but you also have to past a Will -1 test and discard 2 allies, which the crown makes hard to keep.

Haven't run into Serpent Crown yet.

I mean, I'm all in favor of mystery variety that does something different. Getting an artifact was something different. But then 1 clue per investigator (all concentrated on a single investigator), a requirement which makes up the entirety of other mysteries, on top of that? Not all mysteries can be exactly equal in difficulty, but Voice of Azathoth just feels like a blatant middle finger.

Serpent Crown: becomes much easier with Leo Anderson's special action.

Voice of Azathoth: can honestly say I've never had any issues with it. Spread out your investigators and farm the active expedition as much as possible - if you have your investigators sitting on investigation spaces (becomes easier with more players - I 4-investigator games) then you've got a good chance of solving multiple AEs on the same turn as the token moves around.

As for clues, if you just need clues in general then Jacqueline Fine is fantastic - she can trade clues remotely and once per turn she can gain a clue if a non-common condition is handed out to another investigator (and let's face it, in Eldritch Horror those conditions get handed out each turn!).

For me, one of the hardest mysteries I've had to face is the one where you need to close gates that match the omen. Requires you to let the omen reach those open gates which will advance doom and then you have to succeed at closing it otherwise you miss your shot for 1-3 turns. We had this come up along with the rumour that prevents you from closing gates... we lost