An important question on diets has been not only what herbivores eat, but also predators. The same sequencing approach that is used for herbivores can also be used for predators.
It does get more complicated when we shift to predators. First, there are no universal barcodes for all animals. Generally, the approach is to use one barcode for invertebrates and another for vertebrates. Sometimes, a more specific barcode is used that helps resolve other taxonomic groups, like fish.
When sequencing multiple barcodes, there are technical questions about whether to multiplex (PCR the different barcodes together) or run things in parallel.
In addition, when the prey and predator are closely related, predator DNA often gets sequenced. And the predator DNA can swamp out the prey DNA. Predator DNA can be “blocked”, but this approach can be problematic. For example, prey DNA might get blocked, too. Yet, modern sequencing approaches generate enough data that predator DNA can likely be screened analytically.
When all of this is done, the results are less quantitative than what we see for plants. Results really become presence/absence. Or very present-not very present-absent.
Omnivores are a step up in complexity from predators. Here, we move from invertebrates and vertebrates to plants, invertebrates, and vertebrates.
Long story short, predator and omnivore diets have been successfully sequenced in isolated studies a number of times. The best way to approach this in general is still being developed, though. Each case needs to be assessed separately. The techniques used for wolves might be different than bears or feral pigs or mountain lions or eagles.
What is exciting is that we are getting closer to learning a lot more about what the tops of food chains actually consume.