Question for the author: did he really test the map on "Hero" difficulty? The thing is, even if you play optimally, without losing a single unit, and capture the city in the first week, you will have a maximum of 109 ((13+12)*3+7*3+13) archers, 66 ((10+12)*3) swordsmen, 32 peasants ((22*3)-(7*3+13)), taking into account that they are converted into archers, and three knights at the end of the third week. Even after destroying all the monsters in the area, the hero only reaches level 7. In your arsenal of spells, you only have "Surveillance," "Haste," "Slow," "Mines," and "Magic Bolt," which you get after defeating the griffins (which, by the way, you can't do without losses – at best, you'll lose 5 peasants).

These forces are clearly not enough to defeat the Necromancer with 250 archer skeletons, 30 ghosts, 4 Death Knights, and a hundred zombies, especially since he knows "Raise Dead" and has 70 mana points.
If the Castle could be upgraded to a Stronghold or a Castle could be built, or at least archers could be converted into ranged units, there would be some chance, but as it is, even if you manage to destroy the enemy's catapult before it breaks through the walls and cut off the infantry, the constantly resurrected ghosts and skeleton archers will wipe out your entire army.

Of course, there is an idea – not to take the Castle for two months – until you have accumulated several hundred archers and swordsmen, but this is not logical and boring.