There are two endings for this game, one achievement for each. Acquiring these endings is pretty straightforward; at the end of the game there are two doors, left for "blue" ending and right for "red" ending.
If you're reading this guide after you've unlocked one of these endings you will unfortunately have to replay the whole game to unlock the other. But if you're reading this guide before beating the game, there is a way to get both of these Achievements in one playthrough.
As soon as you get the achievement for your first ending hit the
Home button and close the game and restart it. You will have an option to continue from the final room and choose the other door for the second ending.
NOTE: following this method will prevent you from seeing the final cut-scene for the first ending you choose.