The DNS information is pretty neat
How does Dynatrace get it? I have two ideas: through performance counters or through the network npcap module.
I checked the list of performance counters with "Get-Counter -ListSet *" but was only able to find DNS64, but that doesn't seem to get the data that Dynatrace shows us.
So I would say it's grabbed through npcap.
These are of course mine ideas, I believe I have never seen a reference to the "secret sauce"
unfortunately for You, there is not much You can do. Windows (as a DNS client) does not store details on failed/unsuccessful DNS calls in any way.
IF windows is DNS server, then there is option to turn on capturing errors (incl remote DNS calls as propagation goes) and ONLY then You can get more details in it.
Without it only basic metric available, which are giving nothing, except that there is some problem in that area. But without details You can't even know wheter was it some Win internals or Your app that was affected by this failed DNS.
You can always go with full network packets capturing and filter out dns calls - but it's hell of a data and there are tools for that