Portrait photography is a genre that requires very little in terms of equipment. You can get away with even the cheapest camera and lens combination. You don’t even need fancy artificial lights.
The most vital requirement, however, is the use of the right technique. There are several guidelines that help you produce good portraits.
One of them is the basic rule of focusing on the eyes and ensuring that they (or at least the one which is closest to the camera) is sharp.
The next thing is there should be some catchlight in the eyes of the subject being photographed. Sans that the eyes will look lifeless and so will the whole image.
Even with the natural light, it is possible to produce very good images. You can use a white foam core to work as a reflector to add fill-light and cover up the shadows or produce that catchlight.