Dupe your clip and place it above the original.
Convert the dupe to black and white.
Change the blend mode on the dupe to Overlay.
Adjust Opacity to taste.
Adjust saturation of the original (bottom) clip to taste.
To do the whole video at once, either make it a compound clip and do the dupe as mentioned above, or use an adjustment layer - just make the adjustment layer black and white and change the blend mode.