How to backup a container database using RMAN?

To backup the container database , connect RMAN to the root using sysdba or sysbackup.
Note: sysdbackup is a new user introduced in 12c.

After setting the environment variables for the CDB I'm connecting using OS level authentication  (sysdba is already the part of OS group)  as below.

-bash-4.1$ rman target /

Recovery Manager: Release 12.1.0.2.0 - Production on Sat Aug 4 16:50:18 2018

Copyright (c) 1982, 2014, Oracle and/or its affiliates.  All rights reserved.


connected to target database: ORCL1210 (DBID=2368395079)

Now you can take the backup in the same way you take it for non -CDB databases.

RMAN> backup database;

Starting backup at 04-AUG-18
allocated channel: ORA_DISK_1
channel ORA_DISK_1: SID=21 device type=DISK
channel ORA_DISK_1: starting full datafile backup set

channel ORA_DISK_1: specifying datafile(s) in backup set

*********************excerpts*********************

Starting Control File and SPFILE Autobackup at 04-AUG-18

piece handle=u01/app/12.1.0.2/oracle/product/12.1.0.2/dbhome2/dbs/c-2368395079-20180804-02 comment=NONE

Finished Control File and SPFILE Autobackup at 04-AUG-18

RMAN>

Now, Can we backup pluggable database in same session ?  

Yes , I checked it , see below. Please make a note to use the keyword "PLUGGABLE" when backing up the pluggable database.

RMAN> backup pluggable database pdb1;

Starting backup at 04-AUG-18

using target database control file instead of recovery catalog

allocated channel: ORA_DISK_1

channel ORA_DISK_1: SID=42 device type=DISK

channel ORA_DISK_1: starting full datafile backup set

channel ORA_DISK_1: specifying datafile(s) in backup set

**************excerpts*****************

piece handle=/u01/app/12.1.0.2/oracle/product/12.1.0.2/dbhome2/dbs/c-2368395079-20180804-03 comment=NONE

Finished Control File and SPFILE Autobackup at 04-AUG-18

RMAN>

Hope it helps.