I find it easiest to start with the bottom left corner because then you can use the gap next to the USB port to gain a bit of grip and pull that corner apart.
Then take something thin and solid (e.g. a metal ruler like @spinal suggested) and use that on the bottom right to get the bottom half completely loose, then you can do the top two ‘arms’ in either order.
You shouldn’t need to loosen it much to be able to reorient the buttons.
As long as there’s a decent gap you should be able to hold the Pokitto with its back to the ceiling and rotate the buttons with your finger until the little tabs fall into place, then you can seal it up again, keeping the buttons facing down so they don’t move by accident.