how to reach level 20 by the fourth week?

In the neighboring thread, someone very rightly pointed out that you should try to invest in defense with bonus damage. Pyrokinesis, Lucky Sorcerer, and fire resistance are clearly not essential skills; if you do invest in them, do so as a last resort. They won't help much when breaking through defenses.
Also, if your focus is on speed, I think you're taking Erling for no reason. He might be useful for the final battle, but for breaking through defenses, Ingvar is better. Or maybe Ibba, but she's a little worse in my opinion.
Be more aggressive, take risks. Save time: return to the castle less often. That's about it... Don't neglect logistics if you get the chance.