1. To connect to the mysql database to explore what database to backup:
mysql --host=$host --user=$user --password=$password
2. Once connected you can list all databases.
show databases;
3. To backup the particular database, run the 
mysqldump command to write the dump to a file.
For Linux, macOS, or Unix:
mysqldump -h source_MySQL_DB_instance_endpoint -u user -ppassword --port=3306 --single-transaction --routines --triggers --databases database database2 > path/rds-dump.sql
 
For Windows:
mysqldump -h source_MySQL_DB_instance_endpoint ^ -u user ^ -ppassword ^ --port=3306 ^ --single-transaction ^ --routines ^ --triggers ^ --databases database database2 > path\rds-dump.sql