I am currently doing my Masters in Neuroscience and applying for a PhD in neuroscience and had a research project component (50%) but my supervisor is close to retirement and sort of unaware of the system of LORs and how strong they need to be/how they need to be written. I have a really good one from one of my academic professors and I have asked my supervisor and she said yes, but she's been sitting on it and hasn't done it yet. I do however have really good recommendations from my undergrad - college principal/head of department and a professor. Could I use those? Or should I submit an above average one from my supervisor (if she gives it to me, I know she'll just say that I did good work and finished the project - no personal references etc). Or should I try getting another academic one from one of my masters professors?
I doubt that your supervisor has managed to work through their entire academic career without developing knowledge of how to write a letter of recommendation. The best thing you can do is to get in touch with them again and re-iterate that you would like them to write you one. If they still hold off from doing it then definitely use your fallbacks.