Here is the full list of all 40 The Last Flame achievements.
Win a run on Adventurer
Win a run on Adept
Finish a fight with a hero having at least 5000 Max Health
Win a run on Novice
Finish a fight with a hero having at least 1000 Damage per second
Finish a fight with a hero having at least 500 Heal/Shield per second
Finish a fight with a hero having at least 400 Spell Power
Finish a fight with a hero having at least 400 Defense
Get 50,000 gold (total)
Kill 5000 enemies (total)
Craft 100 legendaries (total)
Win a run on Flame Master
Reach Floor 20 on Adept
Reach Floor 20 on Adventurer
Reach Floor 20 on Flame Master
Finish the third act without forging
Finish the third act with at least 2500 gold
Finish the third act with at least 65 trophies
Kill a Dark Dragon
75% codex completion
100% codex completion
Finish a fight with a hero having at least 500 Attack Damage
Defeat The Last Flame
Win a run on Challenger
Reach Floor 20 on Novice
Reach Floor 20 on Challenger
Complete the Wildflame challenge
Complete the Megalodon challenge
Complete the Hardcore challenge
Complete the Hero-ndomizer challenge
Complete the Pacifist challenge
Complete the Boom challenge
Complete the Cloned challenge
Complete the Transcend challenge
Complete the Crazy Hex challenge
Complete the Flame Carrier challenge
Complete the Twins challenge
Complete the Wicked Gold challenge
Complete the Relic Squad challenge
Complete the Impossible challenge