Here is the full list of all 15 Heroes of Havoc: Idle Adventures achievements.
Unlock Idle Mode - Heroes will continue fighting without you
Unlock the Chest in the Main Menu
Unlock Trial 1 - The Impvasion
Unlock the competitive PVP modes by opening the Dark Portal
Unlock Trial 2 - Rise of the Robots
Unlock Trial 3 - Only Human
Unlock Timed 1 - The Hunted
Unlock Timed 2 - Dungeons and Dragons
Unlock Timed 3 - The Green Meanies
Unlock Crusade Mode
Unlock Elite Campaign
Unlock the Visting Merchant
Unlocks the ability to upgrade your equipment
Unlocks the mysterious power of Relics
Unlocks the ability to upgrade your heroes' rarity