In case someone has still the same problem as OP of MySQL using older password hashing method, then the recommended practice is to change the passwords as pointed here.
If at the moment the above is not possible and you just want to make your JDBC connector connect to MySQL the old not so secure way, then way to do it in context.xml file is
authenticationPlugins="com.mysql.jdbc.authentication.MysqlOldPasswordPlugin"
Not sure what is the corresponding JDBC syntax.
Since mysql-connector-java-5.1.19 (latest one I have is 5.1.23) JAR, the default authentication is com.mysql.jdbc.authentication.MysqlNativePasswordPlugin
, so you are basically changing the authentication mode from the default to older one through the above mentioned snippet.