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