When it comes to focus stacking with high magnification objectives, everything that can reduce vibration counts. Among all the things, one common factor, and is well known by many experienced focus stacking experts, is the mirror lockup mode of the camera when using flash to light the subject.
What is mirror lockup anyways? Well, before we get into this, we need to understand how modern DSLR (or SLR for that matter) camera works. DSLR or SLR camera has a mirror that redirects light to your view finder eye piece when not taking a picture. This way, you can see whatever the camera sees (or most of it, like 95% or 98%, depends on camera). When you finish focusing and want to take a picture with your DSLR, here is what happens: the camera first lift up the mirror and then takes a picture. This is a bit brief and if you want detailed information, Wikipedia is our friend -- Single Lens Reflex Camera.
Why is this a problem for high magnification focus stacking? Vibration it causes! Normally, when you take a picture with normal lens, or even a macro lens, vibration caused by lifting up that mirror is minor and might not affect image quality. But when you are doing high magnification stacking, slight vibration can turn into major problem. The process of lifting up that mirror is mechanical and no matter how well it is designed, it will cause mechanical shakes, not just with the camera, but the lens attached to camera. Most high magnification work involves long lenses and tiny shake can cause the lens to bounce around, further reducing image quality.
Here is one comparison: the top image was stacked with mirror lockup turned on when acquiring all images and the bottom one is without. Magnification is about 13.89x and lit with two strobes.
How do we turn on the mirror lockup mode of camera? Most modern DSLRs have this mode of operation but it might be called differently by different manufacturers or even different model of same brand. But if you google "mirror lockup" for a particular camera model, you are more likely to find an answer.
For example, I have a Canon 550D camera, a quick googling yields this: How to Enable Mirror Lockup on a Canon EOS Rebel T3i Essentially, you set camera in one of the mode that support mirror lockup, then set a custom function that either enable or disable mirror lockup. When mirror lockup is enabled, if your press shutter button once, the mirror will be raised and stay that way until you press shutter button again. This is not what we want, to solve this, we need to use the 2 seconds timer. With 2 seconds timer turned on (press Q and navigate to Single Shot, Multiple Shot menu and select 2 seconds timer), when press shutter button, the mirror will be lift up, then you hear some beeping sound and the camera takes a picture after 2 seconds. Though I do not have other Canon cameras, it seems this applies to all Canon models
I also happen to have a Nikon D5200, though if you search mirror lockup, you might end up with sensor cleaning. With that particular camera, the real term for mirror lockup is called "exposure delay" and you can turn this feature on by navigating menu. With Nikon camera (it seems applicable to all Nikon models), things is a little easier, you do not need a timer, when you press shutter button, the mirror is lift up, approximately one second later, picture taken.
Conclusion: if you are using flash to light subject and doing high magnification work (anything higher than 1:1), turn on mirror lockup!