Whew! Your post title scared me a bit but now I understand!
I'm of a mind that literally anyone can be taught to shoot correctly if they are willing to accept proper instruction. I've even taken my blind nephew to the range and had him on paper at 21' with simple muscle memory. So, a sighted person can be taught to shoot accurately. It's a matter of the instructor being able to eliminate as many variables as possible and identify problems. First, you've got to eliminate the variables.
I'll assume you have checked to see what dominant eye she has and that you've made sure that her stance is proper, leaning a little forward, feet spread appropriately to help her maintain her balance and a proper grip on your pistol. Not a death grip but not too loose, either with a proper grip hold, too.
First of all, I'd have the target no further than 21', not 30'. The potential to miss become greater every foot from 21'. I know that doesnt' sound like a lot but where you're trying to fix a problem with aim, getting the target closer helps. Truthfully, if she still has a problem at 21' move the target to 15 feet and work with that. The goal here is to help her build her confidence and to see where her shots are going. It'll be almost impossible to be off the paper so close up. If she can become used to sighting the target close up, she'll be able to repeat it further and further out with more confidence.
Second, don't put up a target at all. Rather put up a large sheet of paper (like 24 x 36") and simply draw a large "X" on it. That helps to see where the rounds are hitting and removes the pressure of scoring. Hopefully you'll see a pattern emerge, too.
Third, that Walther P22 should have a pretty good trigger squeeze and control the recoil pretty well (after all it's only a .22) so the gun, itself, seems fine. I wouldn't rely on the laser, however, and would suggest that you turn it off as it's a disctraction. Rely on iron sites. Have her load and shoot only five rounds, telling her to aim at the center of the 'X' on the paper. At that close range that should be easy so Let's see where her groups go. I assume you've told her to set up the sites so that the front sight becomes the fence post and the target is the pumpkin on the fencepost and to concentrate primarily on the front sight, too.
Finally, some of the problems may be due to where her finger is being placed on the trigger. I've seen more bad habits fixed by that alone. Make sure she is placing the pad of her index finger squarely on the trigger and pulling straight back each and every time. If you have to, draw a line on her finger so she knows where it should go. Putting her finger too far in to out will either pull or push the handgun every time and if she is moving it back and forth that one bad habit could be causing wild shot. Pulling straight back will help maintain a straight pistol with positive, repeatable results. Have her dry-fire as you watch where the muzzle goes when she pulls the trigger.
I'll also add to tell her to memorize where she's placing her shots. Concentrate on each shot as she fires it remembering where the front site was placed. That way when she does hit close to the "X", you can tell her to repeat that same shot again using the same aiming techniques. Once you begin to get a grouping, you'll be able to determine what other minor corrective suggestions to try. ANY grouping will be an advantage here. When there is NO grouping of any kind, that's when it's difficult to fix because there are too many variables happening and you've got to start over again.
Good luck with that! Make sure she's having fun, too!! If it's not fun then she won't want to go again. Above all, don't be critical.....unless you want to go home alone. BE supportive an complimentary when she puts up a great shot. Even if she belittles herself saying things like "I'm not good at this" and the like, be encouraging.
Rome