Depends on whether you want NG+ or not. On nightmare non-NG+ I would say with 99% certainty that it is impossible to do so. On NG+ it might be possible, but I didn't manage it. The main problem is Belphegor and Beelzebub (and likely Asmodeus as well) boss battles and their 100 day limit. It is possible to beat either without SK-ing, Beelzebub being the harder one to pull of, but I didn't quite manage to fit both in the same playthrough. And since I was SK-ing one of them and 100 days mark usually passed by that point I was also SK-ing Asmodeus every time, so Idk how difficult he is to non-SK.
The linked guide above is for normal difficulty. Which is significantly easier to try no-SK run with, I can easily believe it to be possible there. There was another guide for nightmare no-NG+ at some point, but it was made pre slime feeding nerf and was also using SK liberally.
If someone manages to write a guide for max score no-SK nightmare difficulty run, I would also be interested to check how it can be done.