Under-slab waterproofing has some very unique challenges.
There are really just two options: either put a sheet/rolled waterproofing membrane under the the slab, or use chemical admixtures such as Xypex and Concur to waterproof the concrete and block vapor transmission.
We have installed full underslab and under footing membrane systems. These systems tie into your foundtion waterproofing.
We have also used Xypex (which can typically save 50% of the cost compared to a sheet/rolled membrane).
Both are viable options.