I only know HoMM2's original campaigns (Archibald and Roland) which I enjoyed for their variety of challenges. They are long campaigns - if I remember correctly [EDITED HERE] 8 or 9 missions to complete in each chosen from 11 and 10 respectively. (Archibald's 11 comprise 6 that must be played, 1 optional to earn what will be a really worthwhile advantage for some of the later missions, and 2 either/or pairs. Roland's 10 comprise 7 that must be played, 1 optional to earn what will be a really worthwhile advantage for some of the later missions, and 1 either/or pair.)
Automatic saves when you finish a mission mean you can try both missions in an either/or pair, deciding afterwards which to go forward from.
300 days - game turns on the maps - to finish is "black dragon" score. When beating this (which I've done with both campaigns) then (in each campaign) the first mission was one of my slowest. Usually the computer has the advantage of numbers, but often you start with an advantage of your own, for example some extra, much better troops in the second mission. So make the most of this quickly; the longer you take the harder things can get. Cherry pick nearby resources, go for more distant ones first before the computer gets them, or attack its castles while its heroes are out foraging.
In each campaign, "find the crown" is the one mission you can fail through no fault of your own, if the randomly chosen hiding place is too close to the computer's starting castle - and this one the computer does cheat at, recognising at least the general area to go for from far too few obelisks visited. Fortunately this mission is one of an either/or choice, and done right the alternate mission's pay-off is much more valuable. (That's my opinion.)
Sarafan: Don't be afraid to fight with neutral armies.
- what HoMM2 calls "wandering armies" but I think of as blocking mobs. Some are scripted, but many are random choice of creature, not necessarily hostile - there's a chance they'd rather jump aboard your bandwagon than fight your hero to the death. So my tip is always - well, nearly always - attack them with heroes who have room for recruits. Then if they're more hindrance than help in that army, they may still be worth swapping out to another hero or into a castle garrison.
(This is quite separate from the specialist skill for buying off mobs that decided they are hostile.)
Another tip - you go first. This means if you capture a town on the first day of a new week, you can take the week's new recruits there before the computer has time to.
The consensus on YouTube playthroughs I've watched - still discussing HoMM2 Archibald and Roland - is to have one lead hero who does all the fighting (with one big army) so as to gain maximum levels, while secondary heroes starved of experience not only run the supply chain, but also serve as expendable scouts revealing the map. Against the computer in campaigns, I disagree - a more flexible approach worked for me.