I see this question pop up all the time, so I decided to summarize all the ways to gain the elusive 3* and 4* nonfarmable ascension materials through gameplay. If I miss any, please let me know and I’ll add them.
- Rare Quests (Farholme Pass I, Shiloh Desert, Morlovia, Farholme Pass II, Frostmarch, Shrikewood, and Mount Umber) give a fixed 3* mat on stage 4 and a fixed 5* mat on stage 5
- Challenge Events (Knights of Avalon, Pirates of Corellia, Fables of Grimmforest, Riddles of Wonderland, and Guardians of Teltoc) give 3* and 4* materials in the completion rewards for each tier. They also offer additional mats if you are able to finish in the upper scoring tiers.
- Path of Valor gives a fixed 3* and 4* mat on both the free path and the paid path.
- Season 2 Completion Rewards gives a full set of each nonfarmable material between Normal and Hard modes. Note: you have to complete all provinces and defeat the final boss to get the rewards for completion for each mode.
- Monster chests
- Raid chests
- Titan chests
- War chests
- Mystic Vision
- Titan loot, especially higher * and rare titans
- War loot
- Raid tournaments