Here is the full list of all 39 Core Keeper achievements.
Defeated Igneous the Molten Mass
Defeated Ra-Akar the Sand Titan
Obtained Phantom Spark
Gained 100 skill points in mining
Gained 100 skill points in range
Gained 100 skill points in melee
Obtained Rune Song
Sat on a Caveling Toilet while wearing a crown
Gained 100 skill points in running
Gained 100 skill points in vitality
Gained 100 skill points in crafting
Defeated Malugaz the Corrupted
Gained 100 skill points in cooking
Defeated Morpha the Aquatic Mass
Reached max level on a pet
Defeated Omoroth the Sea Titan
Defeated Azeos the Sky Titan
Defeated Ivy the Poisonous Mass
Gained 100 skill points in gardening
Equipped the Ring of Rock and Ring of Stone
Harvested a golden plant
Defeated The Hive Mother
Defeated Ghorm the Devourer
Defeated King Slime
Hatched your first pet from an egg
Defeated Glurch the Abominous Mass
Fed cattle
Gained 100 skill points in fishing
Obtain the Oracle Card deck
Obtained Soul Seeker
Talked to a Big Larva
Caught a Starlight Nautilus
Gained over 200% movement speed
Discovered 100 recipes in the cook book
Planted 10 Cherry Trees
Play the Tune of Tempest
Stored all color variations of one pet type in a chest