Here is the full list of all 15 Reroll: Back to the throne achievements.
Defeat Snowman boss
Find a witch lair
Choose your way
Collect 100 coins
Buy something from merchants
Defeat Chicken boss
Die first time
Try some yummy food
Grab your first coin
Defeat Snake boss
Defeat last boss
Find a secret skeleton stash
Die 10 times
Um, is that binary code?
kazik on the bottle