Here is the full list of all 15 Flamebound achievements.
Finish Room 10
Finish Room 25
Finish Room 50
Finish Room 100
Finish Room 150
Own 3 Heroes
Own 10 Heroes
Sacrifice and Create Rank 2 Hero
Sacrifice and Create Rank 5 Hero
Sacrifice and Create Rank 6 Hero
Sacrifice and Create Rank 7 Hero
Sacrifice and Create Rank 8 Hero
Sacrifice and Create Rank 9 Hero
Sacrifice and Create Rank 10 Hero
Reach 1 Million Gold