Here is the full list of all 24 Flamebreak achievements.
Fight your way through the Furyborn Crags and slay Furere, God of Rage
Complete the loot hook minigame with a perfect score twice in a single run.
Fight your way through the Plane of Precipitance and slay Sepicles, God of Speed
Fight your way through the Worldfire Peaks and slay the Phoenix.
Complete the treasure defense minigame without losing any treasure or allowing a single goblin to escape
Flawless clear 3 minibosses in a single run
Obtain 40 favor with Furere, God of Rage
Fight your way through the Realm of the Undead and slay Necrus, God of the Undead
Fight your way through the Grove of Renewal and slay Halarin, God of Healing
Fight your way through the Steelclad Stronghold and slay Proctus, God of Protection
Kill Necrus, Sepicles, Halarin, Furere, and Proctus
Win 5 games in a row in Hard Mode.
Deal 50,000 damage with a single hit.
Win 5 games in a row in Normal Mode.
Complete the Dwarf's Quest.
Complete the Elf's Quest.
Complete the Human's Quest.
Complete the Minotaur's Quest.
Complete the Faerie's Quest.
Complete the Giant's Quest.
Complete the Halfling's Quest.
Complete the Lich's Quest.
Complete the Zombie's Quest.
Complete the Orc's Quest.