Unfortunately, it seems that implementing this is far from being in the works. Bornakk has confirmed that Achievement Points are "simply a marker of progression in the game" and that there are no current plans to work in a way to spend them.
How do you feel about this? Personally, I was hoping for the eventual vendor selling items like walking canes, pinwheel hats and walking-speed pogo sticks. Still, not being able to spend my points will not stop me from collecting them!