It is not just as simple as taking a section of the database. A lot of the tables are tied in together.
Best way is to make a backup of all your forum files and your database. Be sure to make a copy of config.php.
Now rename your forum folder from phpBB2 or whatever it is called to something like "backup"
Now ftp the complete new phpBB2.0.22 directory to the root of your webspace.
Now rename it to what your old one was.
Now replace your old config.php to overwrite the blank in the new files.
Now run the file install/update_to_latest.php with your browser.
Now delete the install and contrib directories.
You can then add any styles you might want and any mods you want.
Don't worry about the mod related tables that are in the database. phpBB2 does not care about them being there so why should you.
The truth is out there.
Unfortunately they will not let you anywhere near it!