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 ate all the cookies
You pushed a block into the fireplace... for some reason
You womped 100 patrols
You womped 1 patrol
You beat the game without womping any patrols
You visited every house
You left the house in a box
You beat the game without eating any cookies
You beat the game