First few runs that you get to masters don’t try to defeat them. They will be much easier later. Focus on leveling up your primary school to gain more bonuses for research and production.
There should be Abandoned Lab area before completing the Thunder tower, make sure you complete it.
Switch to mana regen equipment instead of attack focused. Living Wood Staff->Silver Staff. Wizard Robe (from story)->Elder Wizard Robe->Archwizard Robe->Wondrous Robe (may need to farm some sheep in special areas which you unlock in Upgrades).
It gives you extra mana regen which you can use to either automate some spells, like Shield of Magic (and later – Safety Wall) in Protection or maybe automate evocation spells (especially Nature element as others will be too difficult to automate this early) or to increase production significantly by casting conjuration spells (leave battle when you focus on conjuration so that you don’t spend mana on evocation spells). Fight manually by using evocation spells after adding evocation and protection (heals) spells into favorites.
Don’t try to automate both production and combat at the same time. You won’t have enough apprentices and mana regen for both at that stage of the game. Don’t try to automate too many boost spells, only choose what you actually need, like mana regen, regen and defense.
Check Stats for Evocation school to check when you can unlock next spell and maybe switch researchers to it to unlock it faster.
In this game trying to progress by fighting in zones works only in early game. In later (after the forest until almost the end) I had to fight manually. There were not enough apprentices to automate combat and trying to kill enemies with weapons took too much time compared to just casting few evocation spells.
Certainly don’t forget to automate Enchant Mana Geysers and Enchant Mana Sprouts with 2 and 3 apprentices respectively for permanent boost.
Rest a day, come back and spend all Time Pieces on research after moving all researchers to primary school. Retire to collect research speed and production speed bonuses. Coming back to the same place with increased production speed and mana regen will be faster and dealing with enemies will be easier. Also with higher bonuses you can get next primary school even higher. Switch schools to different ones each time so you can increase the bonuses even higher.
For bosses craft some potions and use them. They give minor boosts but sometimes those minor boosts are really helpful and let you overcome the boss.