Bulk EML to PDF with attachments handled is a well served need, and the attachments not just lost part is the requirement that separates good tools from bad, so:

The dedicated converter route: tools like SysTools EML Converter take a folder of EML files and output PDF in bulk, with the attachment handling being the feature to check, the good ones either embed attachments into the PDF, append them as additional pages where they are printable or extract them alongside into the same folder, rather than silently dropping them. This is the built for purpose answer for hundreds of files, with a naming scheme keeping each PDF matched to its source.

The Thunderbird route, free: import the EML files into Thunderbird with ImportExportTools NG, then that same add-on exports the folder to PDF in bulk, and its export attachments operation pulls the attachments out separately, the two operations together giving you PDFs plus a folder of attachments, matched by the naming. Free and capable if you have or will install Thunderbird.

The scripted route for control: a Python script parsing each EML, rendering the body to PDF with a library like weasyprint or pdfkit and extracting attachments to a subfolder, gives exact control over layout, naming and how attachments are referenced, worth it for a standing archive process where consistency matters across future batches.

The attachment decision to make deliberately: embed into the PDF for a single self contained file per email, best when the archive should be one file per message or extract alongside for separate access to the original attachment files, best when the attachments need to be usable as files rather than viewed in a PDF. State which the archive needs before converting hundreds, since the two produce quite different archives and redoing hundreds to switch is the avoidable rework.