Very long ago, there was an event which allows getting the Stony and Carbonadium cores.Otherwise, it is purchase from Store.
Is that the only way???
Is that the only way??? Stop spending money/units on potions/crystals/etc to get through Act-5 with a weaker roster and mastery setup, and spend that towards your Mastery instead.It will go a long way towards helping you avoid spending as much later on.
You can get green cores from completing the classic variants (except variant 1).The others you have to buy with units. This is the most barebones masteries you need to be effecient with the game.Beyond this I would suggest going the Despair/deepwounds/assassin route.