Here is the full list of all 36 Cavern Kings achievements.
Collect every trophy.
Unlock every powerup.
Defeat the final boss.
Unlock every character.
Unlock every weapon.
Restore 200+ health as Rex in a single life.
Hit 20+ enemies with a single harpoon shot.
Collect 2+ Spreadshot while using Nailgun.
Reach a depth of 5,000.
Collect 3+ Cluster of Iron with Sawlauncher.
NEW_ACHIEVEMENT_DESC_1_13
Die a total of 25 times.
Hold 10,000+ gems.
Kill The Observer.
Kill a "fire trail" elite monster.
Gain 200+ maximum health.
Collect every Golden Gun.
Kill an "electric" elite monster.
Survive for 5 minutes in Arena.
Kill a boss within 2 minutes of starting a run.
Kill Giga Mechworm in Arena.
Kill The Observer in Arena.
Hold 25,000+ gems.
NEW_ACHIEVEMENT_DESC_1_26
NEW_ACHIEVEMENT_DESC_1_27
Delve deep into the caverns without a gun.
Collect any insectoid powerup.
Find and open the green egg.
Collect 3 Djinn Zephyrhorns in a single life.
Kill a total of 10 Giga Mechworms.
Die a total of 50 times.
Kill a total of 20 Titan Bloodworms.
Collect 3 Black Hole Boxes in a single life.
Die underwater.
Survive for 10 minutes in Arena.
Collect 2+ Volcanic Bombs in a single life.