I don‘t know how to retrieve single events in json format. But you can get complete calendars in jcal format with (jcal = json for iCalendars):
https://NEXTCLOUD.URL/remote.php/dav/calendars/USERNAME/URI?export&accept=jcal
where URI for the desired calendar can be looked up in the database table oc_calendars (your table prefix might differ from oc_).
Of course you also need to authenticate with username and password in the request - I would not put the user credentials in the URL though.