Here is the full list of all 9 You Must Become A Lich achievements.
Have 1000 Coins in the Bank
Open 100 Prize Chests
Have 1 Gem in the Bank
Open ten Prize Chests
Have 100 Coins in the Bank
Open your first Prize Chest
Have 5000 Coins in the Bank
Have 10 Gems in the Bank
Have 100 Gems in the Bank