Looks like we are well on our way to achieving that and nailing the coffin shut on Local Realism..... or are we?
The paper published last week in PRL seems to point to the possibility of a loophole-free Bell experiment. While entanglement experiments with photons have closed down the locality loophole, and experiments with "particles" such as protons, neutrons, etc... have closed down the detection loophole, no experiments have managed to close both of them simultaneously.
This experiment with Yb+ atoms is well on its way to getting there. While they have certainly closed the detection loophole, they have reduced the possibility of the locality loophole by separating the atoms by 1 m (previously, the spatial separation was of the order of microns). So this is a tremendous improvement.
Eventually, it will be convincing enough, if it isn't already.
 D.N. Matsukevich et al., PRL v.100, p.150404 (2008).