I thought you might be interested in how I did it, since the concept is pretty general and I can't remember it being discussed in the forums here.
The image we're talking about was originally posted by daemonoropsis (Morten Aagaard) as image #3 in his topic "First season stacking, my 10 favorites + setup". Other versions and more information can be found on his website, http://mortenaagaard.com/focus-stacking/.
As it appeared in his photomacrography.net post, the image looks like this:

This image looked great to me, but I could see a problem looming.
As posted, the image was 1024 pixels wide. That made it big enough for most of even the small ommatidia to span 4 pixels or more. That's generally considered to be a safe ratio for avoiding aliasing problems.
But our front page format requires images that are only 621 pixels wide.
At that reduced size, the small ommatidia would span only about 2 pixels, and that's well known to be a recipe for disaster in the form of moiré effects. (For discussion and illustration, see "On the resolution and sharpness of digital images...".)
A quick test confirmed the problem, so I asked Morten for a copy of the full-sized image to play with.
Let's start at the beginning. Here's a crop from that full-sized image.

As you can see, it's gorgeous. Crisply delineated throughout, with uniformly sharp rendering of the ommatidia and the "fur" on neighboring surfaces. Beautiful, simply beautiful.
But when we pull that image into Photoshop and do a simple Image > Image Size... > Resample Image: "Bicubic Sharper (best for reduction)", here's what gets produced:
Bicubic Sharper

There's a significant amount of moiré in the eye, certainly much more than I'd prefer to put on our front page.
Now I grant that it's not bad compared to some of the alternatives. Here are resizings with "Bilinear" and "Nearest Neighbor (preserve hard edges)".
Bilinear

Nearest Neighbor

OK, clearly this is going in the wrong direction. Rather than sharper, what we want is smoother. Here are resizings with "Bicubic (best for smooth gradients)" [the default method] and with "Bicubic Smoother (best for enlargement)".
Bicubic [default]

Bicubic Smoother (best for enlargement)

Ironically, it's the "best for enlargement" method that actually does a better job for reducing the eye. But we can do even better than this.
The key to minimizing aliasing is to work with the original size image, filter out any spatial frequencies that cannot be represented in the final smaller image, and then do the actual reduction. By filtering the original size image, we give the filter enough information to do its job accurately.
The exact filter we need is not available in Photoshop (or if it is, I don't know where).
But a reasonable approximation is provided by Gaussian Blur with a width that corresponds to about 0.5 pixels in the reduced image.
In this case I'm producing an image of 641 pixels from a starting image that's about 5 times bigger, so I'll use a Gaussian Blur of 2.5 pixels (2.5/5 = 0.5).
When applied to the original image, the first thing we see is so badly blurred that it looks like complete junk:
original plus Gaussian Blur of 2.5 pixels

But this blurred junk version is just the pre-filtering we need to get a lot less moiré after resizing!
With this pre-filtering, here is what gets produced by "Bicubic (best for smooth gradients)" and "Bicubic Sharper (best for reduction)":
prefiltered, then Bicubic

prefiltered, then Bicubic Sharper

That last one looks pretty good, at least on the eye. There's a very small amount of moiré left, but nothing I'm motivated to go after, and in general the eye presents an appearance of sharpness that strikes me as representing well the original image.
However, when I go back and look at the rest of the fly, I'm not so happy with the overall sharpness. It strikes me as too soft, not well representing the original.
Of course moiré is not a problem on the rest of the fly, because there are no repeating patterns to make aliasing visible.
So, I can cheat ... um, "have my cake and eat it too" ... by using some simple layers and masks to merge the best rendition of the eye and the best rendition of the body, each in their respective areas.
For the eye, I like what we've done above, and for the body I like what's produced by my usual process of "Bicubic" resizing followed by Unsharp Mask of 35% at 0.3 pixels to add a bit of bite.
Here is the result of the merge:
final merged image

This may look like quite a bit of trouble, but really the process went a lot faster than it takes to tell about.
Besides, I think it's worth putting in some time to make our front page image look good.
I hope this is helpful.
--Rik