Here is the full list of all 22 Dice Assassin achievements.
Die for the first time
Complete the first level
Reach level 5
Reach level 10
Arrive at the store for the first time
Kill one rat
Kill one bat
Kill a frog
Complete a level without taking damage
Defeat the Face to face
Pass your turn
Collect 50 coins
Kill any enemy with one hit
Kill two enemies with a single attack
Buy a new weapon
Take the same number on both dice at the same time
Complete the tutorial
Use one card
Make an enemy kill another
Kill any enemy with another weapon
Improve your attack dice
Improve your range dice