Here is the full list of all 70 Heroes Of Hellas 4: Birth Of Legend achievements.
For restoring 7 Hero mosaics without using "Solve"
For completing 20 levels without quitting
For collecting 400 gems
For using Heroes' help 500 times
For collecting 10,000 gold while playing Helios' Treasure levels
For completing 80 levels without Hermes' help
For collecting 1,300 golden tiles
For collecting 150 treasure chests
For playing for 500 minutes
For hitting 4,500 coins
For destroying 2,500 monoliths
For collecting 200 Phoenix feathers
For making 5,000 chains
For removing 1,000 storm clouds
For using Heroes' help 200 times
For collecting 100 Phoenix feathers
For hitting 15,000 tokens
For hitting 2,000 coins
For completing 40 levels without Hermes' help
For restoring 3 Hero weapons without using "Solve"
For collecting 150 gems
For restoring 3 Hero mosaics without using "Solve"
For using Heroes' help 30 times
For activating 500 bombs and lightning bolts
For removing 100 Earth tiles
For collecting 30 treasure chests
For completing 20 levels without Hermes' help
For making 1,000 chains
For hitting 3,000 tokens
For watching the Pantheon of Heroes for one minute without moving
For collecting 20 gems
For hitting 300 coins
For destroying 80 monoliths
For activating 30 bombs and lightning bolts
For collecting 30 golden tiles
For agreeing to help Hermes
For playing for 1,500 minutes
For completing 60 levels without quitting
For beating every story monster
For hitting 50,000 tokens
For making 15,000 chains
For removing 1,000 Earth tiles
For removing 1,500 Earth tiles
For destroying 6,000 monoliths
For removing 2,000 storm clouds
For collecting 3,000 golden tiles
For collecting 250 treasure chests
For collecting 400 Phoenix feathers
For activating 5,000 bombs and lightning bolts
For restoring 7 Hero weapons without using "Solve"
For passing 10 levels in half the given time
For passing 30 levels in half the given time
For passing 90 levels in half the given time
For collecting 20,000 gold while playing Helios' Treasure levels
For collecting 50,000 gold while playing Helios' Treasure levels
For collecting 3,000 gold while playing a Helios' Treasure level
For collecting 5,000 gold while playing a Helios' Treasure level
For collecting 7,000 gold while playing a Helios' Treasure level
For passing 30 levels in one third time
For defeating every monster in the "Heroes and Monsters" gallery (Normal)
For defeating every monster in the "Heroes and Monsters" gallery (Advanced)
For defeating every monster in the "Heroes and Monsters" gallery (Legendary)
For completing the game with no timer
For completing the game with the timer
For completing the game without Hermes' help
For freeing Zeus
For solving 5 puzzles
For solving 10 puzzles
For solving 15 puzzles
For completing the construction of Zeus' park