After installing any version of the Oracle client, including SQL Developer, Duo multi-factor authentication requires a setting in the sqlnet.ora file. Clients without this setting will see the error ORA-01017: Invalid username/password when trying to connect.
The sqlnet.ora file must be placed in the installation directory or in a directory specified by the environment variable TNS_ADMIN. For Instant Client installations, it is best to just place it in the instantclient directory. If there is no sqlnet.ora file on your computer, create one in that directory using a text editor such as Notepad.
Manually Editing sqlnet.ora
Once the file is created and open in an editor, add this line:
SQLNET.AUTHENTICATION_SERVICES=(RADIUS, NONE)
Optionally, but not required for Duo 2FA to work, you can add the following line to make database connections over the UMN VPN more stable:
DISABLE_OOB=on
NOTE: Beware of Notepad on Windows adding a ".txt" extension to the file when saving it. It might try to save the file as sqlnet.ora.txt, in which case you should rename it to simply "sqlnet.ora."
Obtaining sqlnet.ora From GitHub
The Oracle DBA team provides a sqlnet.ora GitHub repo which contains the current configurations for the University of Minnesota. You can always use this to create/update your local files.
SQL Developer Configuration
SQL Developer requires an additional step to work with multi-factor, as described in Installing the Oracle Instant Client & SQLDeveloper.