I made a few tests to determine what is needed to get the best score. The difficulty you set is directly correlated to your final score. Also, you won't achieve Black Dragon rank if you only choose maximum difficulty for the last mission. Rating seems to depend on an average for all missions which makes sense. So, to get the best score, you need to choose Impossible difficulty for all missions.

After doing it for the Master of the Elements Chronicles campaign I found it not too hard to achieve. You don't get resources at start but it's really just a slight delay. Gold becomes much more important though and heroes that give some on a daily basis have high value.

AFAIK all the older (don't know about the new ones) HoMM games' scores are based on difficulty level and time (game days) used.

Even the regular M&M games use amount of game days spent (amongst other things) to calculate the score, which is something I personally really appreciate.

Incidentally I got a score of 2115 in Master of Elements, myself.
But the Chronicles are so easy that the difficulty level doesn't matter much (compared to HoMM 2-3 stand alone maps), what with the overabundance of resources strewn about the maps.

I guess you're right. I've not played HoMM 2 & 3 for a long time and I never played scenarios.
I'm doing the 4th chronicle (Elves & Dragons) and this one is quite difficult on Impossible. It's precisely small maps where resources are not so numerous that are harder to finish.