The museum collection includes minerals and artifacts. Note that the items have to be donated and not just found (your collection guide will show them as soon as you find them). The only way to know if you haven't donated something is that the text, "Gunther can tell you more about this..." will appear when hovering over the item.
Artifacts are found purely by chance; the game will also choose two random artifacts and make them extremely rare so this achievement can be fairly difficult.
Here's a spreadsheet to help you keep track of the artifacts you've donated:
https://docs.google.com/spreadsheets/d/1rTxEvKUFmRDS4l8px_84...(Minerals are much more plentiful so I didn't include them on the spreadsheet).
Once you've donated everything possible the next day you'll get a letter from Gunther with a stardrop enclosed.