Here is the full list of all 31 Incremental Epic Hero 2 achievements.
Perform Tier 1 Rebirth once on any heroes
Unlock Spider Maze
Unlock the 3 heroes from IEH1 - Warrior, Wizard and Angel
Unlock Magicslime City
Complete all the tutorial quests
Unlock all 6 heroes - Warrior, Wizard, Angel, Thief, Archer and Tamer
Unlock Bat Cave
Unlock Fairy Garden
Unlock Fox Shirine
Unlock Devilfish Lake
Unlock Treant Darkforest
Unlock Flametiger Volcano
Unlock Unicorn Island
Vanquish a swarm
Vanquish swarms 10000 times
Reach Total Potion Level 1250
Reach Total Potion Level 3000
Have 8 Class Skill Slots on any heroes
Have 8 Global Skill Slots on any heroes
Perform Tier 2 Rebirth once on any heroes
Perform Tier 3 Rebirth once on any heroes
Perform Tier 4 Rebirth once on any heroes
Perform Tier 5 Rebirth once on any heroes
Perform Tier 6 Rebirth once on any heroes
Perform Tier 1 World Ascension once
Perform Tier 2 World Ascension once
Perform Tier 3 World Ascension once
Walk 40,075 km in total
Walk 384,400 km in total
Open 10000 Tresure Chests
Spend more than 10,000 Epic Coin at Epic Store