Here is the full list of all 40 The East New World achievements.
Collect 10 crystal fragments
Collect 10000 Gold Coins
Collect 100000 Gold Coins
Clear level 8 in Chap. 1 without killing any enemies
Clear level 8 in Chap. 2 without being hurt
Collect 17 suits of armor
Collect 20 weapons
Collect 24 Relics
Pass level12 in Chap.3 without collecting coins
Kill the Ancient Mummy
Kill Anubis
Vanquish the Colossus Crab
Defeat the Giant Piranha
Extinguish the Lava Giant
Slay the Fire Dragon
Kill 1000 enemies
Kill 5000 enemies
Kill 10000 enemies
Kill 20000 enemies
Clear level 12 of Chap.1 without using magic
Avoid the Rock Giant's pummeling 5 times
Escape the Merfolk's grasp 4 times
Evade the Fire Lizard's scorching heat 3 times
Collect all treasures in Chap. 1
Collect all treasures in Chap. 2
Collect all treasures in Chap. 3
Collect all treasures in Chap. 4
Collect all crystals in Chap. 1
Collect all crystals in Chap. 2
Collect all crystals in Chap. 3
Collect all crystals in Chap. 4
View the Good Ending
Clear level 3 perfectly in Time Rush
Clear level 6 perfectly in Time Rush
Clear level 9 perfectly in Time Rush
Collect 20 crystal fragments
Collect 30 crystal fragments
Collect 60 crystal fragments
Defeat the Succubus
Slay the Corrupted Knight