Here is the full list of all 10 Hail to the King: Deathbat achievements.
You completed the tutorial!
You talked to an NPC!
You talked to all the NPCs!
You beat the game!
You beat the game in Nightmare Mode!
You beat the game without losing a life!
You beat the game in Nightmare Mode without losing a life!
You acquired every weapon in the game!
You opened all the bonus levels!
You acquired all of the lost art!