Here is the full list of all 10 Cave Story's Secret Santa achievements. It takes around 1-2 hours to unlock all of the achievements on Windows.
You beat the game without being discovered
You beat the game without womping any patrols
You beat the game without eating any cookies
You ate all the cookies
You beat the game
You visited every house
You left the house in a box
You pushed a block into the fireplace... for some reason
You womped 100 patrols
You womped 1 patrol