Um, I don't think you can do SEO on a PDF file. At least nothing different than using relevant links and keywords in the PDF. If you really want your PDF file to rank for something link to it.
PDF optimizing is not different from optimizing on-page seo (website content). As we know Google can read PDF file like they read on ordinary web page. If you have a unique content written in PDF format then Google would find it and give a rank for it. However, I would saying from my own experiences - Google does not give equal weight toward PDF content compared to ordinary web page content. They have used several factors to judge before give a ranking toward each certain PDF file since this kind of content is too easy to manipulate. They have used domain authority / trust to judge how ranking it should be. This is why you have seen many PDF files has a good ranking under University / Government / Big Non-Profit Organization website more than ordinary website.