There is another way that might be more convenient than dealing with assets and categories table.
First of let me state that:
IDeally you should just update the 2.5 site to 3.4.
This is absolutely true.
But if you do not want to do this upgrade, you can put all your JEvents info in a CSV file and then import this CSV file in the Joomla! 3.4 site.
Unfortunately we do not provide a CSV export facility, but you should be able to create a valid CSV file following this instructions (it also provides a file that you can easily upload and modify to fit your needs):
https://www.jevents.net/docs/jevents/it ... -of-events
The correct format you should import is shown in this document:
https://www.jevents.net/frequently-aske ... csv-format
with special references to Custom Fields data.
Best!!