Here is the full list of all 24 Incremental Epic Hero achievements.
Achieve Lv 100 for all Reincarnation Skills!
Complete all Mission Milestones!
Collect 100 Rainbow Fish!
Achieve all Gems Lv 100 in Dark Ritual!
Fill the skill progress bar (Class Passives) for all 3 classes!
Craft all equipments of Rank A!
Craft all equipments of Rank S!
Complete 3 curses (Road of Warrior 2, Road of Wizard 2 and Road of Angel 2)!
Craft all equipments of Rank B!
Craft all equipments of Rank C!
Defeat Distortion Slime!
Complete Area 8-8!
Defeat Octobaddie!
Defeat Montblango!
Defeat Bananoon!
Defeat Fairy Queen!
Defeat Deathpider!
Defeat Golem!
Defeat Slime King!
Achieve 10,000 Reputations!
Craft all equipments of Rank D!
Complete the tutorial!
Complete all the quests except repeatable ones!
Collect 100 Red Chilis!