It's quite easy to complete:
In the first 3 days, capture the first 2 castles.
Then, with one of the heroes, stay at the base and capture all the mines.
Standard troops are sufficient for this.
With the second hero, buy as many Minotaurs as possible and head to other castles. In 2 weeks (from the start of the mission), you can capture 4 castles.
When capturing every 2 castles, a red hero will appear. He simply heads to a specific city of yours, each time to a different one, so you don't need to intercept him; instead, determine where he's going and wait in the castle.
Then, simply gather an army – it doesn't necessarily need to be large (I didn't build any dragons at all) – and go capture the remaining cities.