Okay - you are getting closer.
Code:
SELECT Max(TransEntries.[TransDate]), TransEntries.[Vendor], TransEntries.[Category], TransEntries.[TransNote]FROM TransEntries
GROUP BY TransEntries.[Vendor], TransEntries.[Category], TransEntries.[TransNote]
Try this as a query and you will see that it nearly gets you what you want.
Hint: As you have multiple categories you will need to actually need another sub query to just return the last TransactionID grouped by vendor and link that back to get the categories and notes.