Currently Office 365/SharePoint online does not support opening PDF-documents directly in the client application (Adobe Acrobat Pro/DC). Instead they are opened in SharePoint’s web viewer. There is a UserVoice suggestion addressing this issue, with a lot of votes, but so far there is no communicated road-map from Microsoft for this feature.
From SharePoint’s web viewer you can open a document in your browser, by clicking on “Open” and the “Open in browser”:
Depending on which browser you use you will be getting different options. The only browser that enables you to open the document in your desktop application is Google Chrome, where you get a floating menu, on the right-hand side of your document, that enables you to open the document in your desktop application:
Unfortunately this option will not give you the possibility to edit the document and save it back directly to SharePoint.