The most challenging campaign.

Haven
This is generally an easy campaign; it shouldn't cause any problems even on Hero difficulty.
Inferno
Also easy to complete. The only difficult mission is the third one, but even that isn't critically challenging if you do everything quickly.
Necropolis
A little more difficult, but not by much. Necromancers are the easiest race to play as overall. The third mission and the second mission are somewhat challenging.
Dungeon
This one is generally more difficult. The third mission is quite challenging at the beginning, but the rest seem to be easy to complete, except for the second mission, which is moderately difficult.
Sylvan
This will be the most difficult of the original Heroes campaigns, but even here, only two missions are difficult: the second and the fifth. But the fifth mission was the most nerve-wracking at the time.
Academy
One of the easiest campaigns; only Humans and possibly Demons are easier, and even that's not certain. At most, you'll have to put in a little effort at the beginning of the third mission when you invade the lands of the Griffin Empire.

Of the expansions, the second mission for the Orcs is also quite difficult. I can't recall any other particularly difficult missions.