When editing people, one of the things fixed more often than not are under-eye circles. Some people have more significant circles than others, and that is okay. Every time I teach a webinar or workshop I encourage attendees to let their subjects be human, meaning let them have imperfections, and under-eye circles are one of those imperfections. However, that does not mean we can't minimize them - that is perfectly okay.
What I Try First
My go-to trick for reducing the darkness or redness of under-eye circles is using the Under Eye Circle brush in the Perfect Portrait brush collection. That typically does all that I need done, meaning it reduces them enough so they are not as noticeable, which is my goal.
My Back Up Method
When the Under Eye Circle brush doesn't work I turn to my handy clone-tool-trick. This is an EASY edit technique, but the key is to use the right "feather" for your subject, and lower the opacity so that it blends in, rather than standout.
Below you can see there area I brushed over with the clone tool, the under eye circle, and below it the area I selected to be the area it replicated. I show how to do this, and give tips for success, in the video below.