If you're playing as a Warrior, you need to take 3 castles in the north and northeast of the map VERY quickly. I took them within 2 weeks of the start of the game; otherwise, you'll simply be overwhelmed by numbers... after that, it will be quite easy. This is on a difficult setting. Regarding skills: Tears are objectively better; the second level isn't necessary. Logistics + pathfinding + pillaging are a must-have, as are all the skills of the Cleric. If you're playing as a Mage, then tomatovv can explain it better than I can.
I tried to follow your advice and it didn't work... I didn't make it to the second castle before I encountered an enemy hero with a deadly army for Anton.