Here is the full list of all 31 Incremental Epic Hero 2 achievements.
Unlock Bat Cave
Perform Tier 1 Rebirth once on any heroes
Vanquish a swarm
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 Fairy Garden
Unlock Fox Shirine
Unlock Devilfish Lake
Unlock Treant Darkforest
Unlock Flametiger Volcano
Unlock Unicorn Island
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