Your initial location:
Put your 3 less important units at the right, so they can block the forts.
In this chapter, your mounted units will dismount until you get past the stairway. Also, bring ice magic; it is effective against the fire dragons.
For your first 2-3 turns, you should take care of the closer fire dragon and the flying dragons that will come towards you. Be careful with their range.
After this, you just have to advance, slowly luring the remaining fire dragons and barbarians. It’s easier than the previous chapter, due to fire dragons having less movement than flying ones.
At the northeast, you’ll find a dragon guarding a chest. Kill it and obtain the last orb fragment. You must have all 12 of them now.
After that, you can go seize the throne.