Here is the full list of all 15 Slime Hero achievements.
You are the Slime Hero.
You get "Azure Dragon" power.
You get "Vermilion Bird" power.
You get "White Tiger" power.
You get "Black Tortoise" power.
You defeat 1 slime enemy.
You defeat 10 slime enemy.
You defeat 100 slime enemy.
You defeat 1000 slime enemy.
You defeat 7777 slime enemy.
you are the master of "Spring" stage.
you are the master of "Summer" stage.
you are the master of "Fall" stage.
you are the master of "Winter" stage.
you are the legend.