"Use a material with better than 99.999% reflectivity. Usually, highly reflective surfaces are dielectric mirrors, which are composed of ‘sandwiches’ of material, with each layer reflecting back a modest fraction of the total. Each layer needs to be at least a quarter of a wavelength thick. The weight can be reduced by using a monolayer with high reflectivity at the correct wavelength. Based on recent research, this could be achieved by a ‘hole-pocked’ layer, highly reflective for very specific angles where reflectivity caustics arise. (These caustics occur for wavelengths of light that are actually longer than the sheet thickness.)"

http://breakthroughinitiatives.org/index.php?controller=Foru...

Upon further reading, looks like you can achieve >99.9998% reflectance for a 10% wavelength band (in this case, in the infrared). [http://www.crystallinemirrors.com/wp-content/uploads/2013072...]

Still, you're right in saying that it's probably still quite a ways off.