Here is the full list of all 15 Slime's Journey achievements.
Defeat the first Boss.
Defeat the second Boss.
Defeat the third Boss.
Defeat the fourth Boss.
Defeat 25 enemies.
Defeat 50 enemies.
Defeat 100 enemies.
Defeat 150 enemies.
Get 25 gems.
Get 50 gems.
Get 100 gems.
Open 1 treasure chest.
Open 5 treasure chests.
Open 10 treasure chests.
Open 15 treasure chests.