I'm currently in the middle of month 2, and I've completely eliminated the red faction with archangels. The "hit-and-run" tactic with explosions didn't give him a chance. I'm planning to use the same approach to take down the Fortress flag, but I'll have to rely on brute force against the black dragons (it would have been better to start with the Dungeon instead).
I think that two flags should be eliminated quickly, while one should be left standing for a bit longer. Then, with a hero equipped with hydras, we deal with the remaining enemy hero and move on to the water.
The author said that on the cross with the Grail, you need to kill the opponent, but it doesn't seem to be essential.