Here is the full list of all 16 Abyss Cave achievements.
Killed first installment of enemies.
Killed 100 enemies.
Killed 500 enemies
Killed 9,000 enemies.
Annihilated over 10 enemies at one time.
Discovered 5 Relic Gears.
Discovered 30 Relic Gears.
Killed 5 dragons.
Killed 30 dragons.
Complete gear upgrades.
Found 3 hides
Completed robot upgrading
Unlocked Medium Turret
Unlocked Missile
Unlocked Advanced Turret.
Till the base is repaired, less than 10 Turrets are damaged