This is my workflow to create creature illustrations for the Bestiary. Follow these guidelines if you want to create illustrations as close as possible to mine in terms of style, for a more cohesive and consistent menu.

1. Download and install the Review Studio mod.

1b. (optional) If necessary, you can install a retexture for the creature, but try to stay close to its original design (unless of course you are making a patch for a retexture or remesh).

2. Start the game and in the console type: coc studio1
You will be teleported to the white studio. Note that for some creatures, a black background works better. In this case, type: coc studio4.

3. Summon the target creature in front of you with: player.placeatme [FormID]
Enable godmode: tgm
Set FOV to 60: fov 60
Depending on the pose you want to achieve, you can use tcai to disable the creature's combat ai.

4. Then it's the fun part. Turn around the creature, bash it (don't attack it or it will be covered in blood, unless that's what you want), run around and freeze the game at different time by opening the console. Type: tfc 1 to enable freecam mode. If you are satisfied with the creature's pose, then find a good angle and press F12 to take a screenshot.
Make sure the target takes a significant portion of the screen for best image quality.

5. Repeat step 4 until you have a few good screenshots to choose from.

6. Choose the best screenshot and open it in an image editor of your choice (I personally use GIMP).

7. One of the trickiest and time-consuming steps, depending on the creature. You have to crop out the background (-> transparency) and only keep the creature itself. The magic wand is the first tool I use, filtering by luminosity and then playing with its threshold until I'm satisfied. For some creatures, for example the Cave Bear over a white background, this will be enough and I'll be able to jump to the next step.
For others, like the Ghost, it wasn't that easy. The Color to Alpha tool is very useful in this case to render the creature's transparency. Over a black background, using Color to Alpha selecting black will do the trick. Again, play with the tool's threshold until you are satisfied with the result.
Finally, the more complex creatures will require using the eraser or lasso to make more precise edits. More than once I have had to repaint some part of an illustration pixel by pixel...
You have to be creative, the goal in the end is to have the creature's image on a transparent background without visible imperfections.

8. Now it's time to apply the Oil Paint filter! I decided to do that for two reasons: 1) it hides small imperfections and makes low res textures less obvious, and 2) gives a subtle but nice hand-drawn feeling to the bestiary.
Try to make it subtle, and adjust the values depending on the image at hand. Some creatures required a stronger Oil Paint filter amount than others to achieve more or less the same look.

8b. (optional) if your image editor of choice doesn't support DDS with BC3 (linear, DXT5) compression, then copy-paste your image to another one (I personally use Paint.NET)

9. Crop your image to a square format, taking into account the in-game size of your creature. For small creatures (e.g. chicken, rabbit), they shouldn't take all the space of the square. Bigger ones (e.g. wolf, sabre cat) should fully occupy the space. And the largest ones (e.g. mammoth, dragon) can be cropped. Of course, this is highly subjective and at your discretion.
If cropping, I recommend cropping the creature on no more than two sides of the square. Having a creature cropped on three of four sides isn't as aesthetically pleasing.

10. Resize the image to 720x720. It is extremely important, as Flash can be somewhat picky about image size and will straight up refuse to display it if it doesn't adhere to its obscure rules. I have found 720x720 to be a good compromise for image quality, and it works perfectly with Flash.

10b. (optional) if the creature was cropped, you will have to add progressive transparency where it was, to avoid ugly, straight cuts. On Paint.NET, I use the eraser tool with size 175 and hardness 9%. I click on the areas near the edges of the image until the blend looks good. Sometimes, I also click a few times on the elements in the background (leg, tail, ...) to give a subtle impression of depths. Once more, this is at your discretion.

11. Save the image as .DDS and make sure to select BC3 (linear DXT5) when prompted.

12. Load the game to check your illustration. You can keep making adjustments in your image editor while the game is running. Save the image and either close and reopen the menu, or select another creature and go back to your target to see the changes. Switching between variants won't reload the image.

Good luck!