It’s possible on your own if you only want to see one of two places - either taking the service bus up to Tobermory or doing the tour out to Fionnphort to see Iona and possibly do the `Staffa boat trip (fab scenery, Fingal’s Cave and potentially puffins.) You can also book that tour in Oban - see link below:
https://westcoasttours.co.uk/book-tour/tour-mull-iona-and-staffa/
You don’t have to do the Staffa trip of course but it is wonderful.
There are organised day tours on Mull mainly focused on wildlife watching , one option in the link below but there are others…
https://www.naturescotland.com/
Otherwise, Mull does not lend itself to getting about without your own car sadly.
There are also whale watching trips going out from Tobermory.I also think some of the Staffa/Treshnish Isles trip operators will pick up from Craignure itself where the ferry comes in but check their websites - Turus Mara or Staffa Tours.Long standing boat trip operators.