There are a lot of potential issues that can arise when shooting HDR images. These problems include camera shake, motion blur, ghosting and more. Using a tripod can help you get the absolute most detail out of your HDR images. If you do not use a tripod, you will not yield the same results and quality when compared to using a tripod.
As mentioned before, to get the most detail out of your HDR images, you need to use the tripod. The reason for this is simple. For example, if we have a camera that shoots at a frame rate of 3 frames per second and we are shooting a standard 3 frame-2 stops bracketed sequence, the quickest our camera can take these 3 images is 1 second because the camera shoots 3 images per second. This does not include the length of time the shutter is open for each shot. This means that in addition to the length of time the shutter speed is open for each shot, we also have to hold the camera perfectly still for an entire second while the camera cycles through each image in the bracketed sequence. In this example, that would be 3 images. Handholding the camera will be absolutely impossible. Even with a quick shutter speed, you will notice a bit of shifting in your images when you bring them into post production and go through them. This shifting, caused by handshake and body movement, will cause a reduction of overall detail when you layer these images, even when the images are properly aligned. You would not get the same kind of quality detail you would want out of that bracketed sequence, so it is important to use a tripod whenever you are shooting HDR photography.
Even if you have a top of the line professional DSLR that can shoot at a high frame rate per second, it is still best to use a tripod. In addition, different scenes may require the use of shutter drag. Shutter drag is where we are dragging the shutter out for 10-30 seconds at a time with the intention of either doing a bracketed sequence or a single-shot HDR. In these situations, it would be absolutely impossible to shoot these images without a tripod to hold the camera completely still.