Here is the full list of all 10 FATE: Undiscovered Realms achievements.
Kill 5 enemies in 15 seconds
Destroy every chest, urn, barrel and wooden box on a single level.
Transform your pet in all the available companions.
Collect all 6 Fate cards in any one set.
Recover and return to the statues all the stolen equipment of the legendary heroes from Druantia and Typhoon.
Complete the game in Hardcore Mode.
Send your pet to town at least 10 times from the 40th floor.
Get 50 critical hits!
Reach the maximum level of Spear Skill.
Use any spell 100 times.