I have been working on a paper that is now ready for submission. I put a lot of time into polishing my figures in Illustrator, which are very detailed bioinformatics visualizations. I sent the figures to the main responsible PI. The PI has now sent me a draft of the manuscript, with the suggested arrangement of the figures. All in JPEG format. A scrutiny of the person's publication record implies that this is also likely to end up being the case for the final product. I realize that the paper has the potential to go fairly high in terms of impact, if appropriate work was put into the presentation. To be frank, none of the more respectable journals today will accept figures presented in this fashion, and if they do it would demand a lot more in terms of the underlying science than some PDF-using competitors might get away with. So, with a reasonable fear of triggering certain latent ego issues (which appear to be quite common among PI:s in academia), how would I go about convincing this fairly established and high profile PI (as an unsignificant Phd student) to fully switch to vector based figure layout?
From the comments I gather that you are afraid to criticise your PI for producing low quality images, which is natural.
I think that a good course of action here would be an e-mail where you tell your PI that your journal requires vector based images. Then you say that you know that he is a busy man and that you are willing to reproduce his images in Illustrator if that is okay with him (assuming the pictures are easily reproducable). That way he will probably thank you for going the extra mile and taking work off his shoulders.
I would refrain from telling him to make better pictures himself, because he has probably done it the same way for decades and it is hard to change such habits.
Good luck with your publication!
While this specific instance obviously has been dealt with, others might find the following useful.
It is professionally acceptable, usually even desired to establish work delivery in certain file formats.
Ideally this is done before work is started or as concerns become apparent.
I see no issue if the quality requested by OP (with third parties like publications in mind) enhances the overall presentation.
In fact, I'm in agreement.
Print publications not only frown upon using lossy compression formats, they have standards regarding resolution as well. Vector formats can be scaled without images becoming pixelated, so are superior to bitmap formats with insufficient resolution.
So to clearly answer the question at hand as well: Politely and neutrally suggesting to adhere to the standards required by print media (as mentioned, research on the site of the journal in question or industry standards) should be enough to convince anyone to prefer certain file formats.