You need to run to the left and up towards the keymaster's tent, collecting all possible troops along the way. There's a portal near the keymaster's tent. Then, you go underground and run to your Castle, gather an army, and complete the mission.

You're wrong! This is in the 4th mission, the Castle is underground!

The 3rd mission is completed as follows: (although I passed it on the 3rd try)

1. We have a main city and a small army. We run to the right on the map and capture the Elven city; this won't be difficult.
2. Next, over two weeks, we develop the cities (while actively moving the hero and collecting resources; you can even hire a second hero for this).
3. Then, we run up the path from our Elven city. To reach the 2nd Elven Castle, we need to defeat 4 Phoenixes. The main thing here is a "more substantial" army so that the Phoenixes don't have enough turns to defeat this army. All 7 slots must be filled! We focus on the hero's magical abilities!
4. We defeated the Phoenixes - very good. We gather an army and run up, capturing the 2nd Elven Castle; this won't be difficult. A weak hero is stationed there, and we are already at a high level =)
5. As a result, we have 3 cities, and the green faction has only one. Draw your own conclusions. We defend the cities, develop them, and don't go anywhere.
6. We hire an Elven hero, level up his DIPLOMACY, and give him all the Elven army we can gather. The nasty Druids start pouring troops onto the roads after the first week. But we have diplomacy and a strong army. We run around and collect. There will be no battles, although we gain experience and an army quickly. I collected about 3,000 sprites, a lot of archers (about 500), and dancing swordsmen (1,500) in a month.
And I raised the Elven hero to level 21.
7. Next, we go, gather all the demonic army with our main hero, give all the Elven army to the Elf. We go to the last Castle. We attack with the Elf, even if he dies, it's not a big deal; we finish it off with the Demon.

That's it.