Can't seem to go beyond after second boss fight@lv8

What’s the required level and what’s the boss level for the third die roll d20?

Varies, depending on which dungeon you’re doing. Have to defeat third boss, and thus complete the dungeon, to receive the d20. The first two or three dungeond have boss every third room. Nine rooms per dungeon. Then it bumps up to every 4th room, so 12 rooms in Heartcoil.