Advanced Search: Exporting Groups/tags fields from event participant search
A possible work around is to do the search twice, first search will be to add the contacts to a temporal group and export contacts with the right tags and groups, the second search, export the events related data and use excel function example Vlookup to add tags/groups to your last export. You may want to export the contact ID, which will be your unique column for Vlookup.

Hope this helps.