With multitenant feature introduced in oracle 12c, New commands are there for taking rman backup of pluggable database and root container database.

Backup of complete container( ROOT + ALL PDBS )
SQL> show pdbs

    CON_ID CON_NAME			  OPEN MODE  RESTRICTED
---------- ------------------------------ ---------- ----------
	 2 PDB$SEED			  READ ONLY  NO
	 3 ORCL 			  READ WRITE NO
	 5 PROD_MN			  READ WRITE NO
SQL> exit
Disconnected from Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
With the Partitioning, OLAP, Advanced Analytics and Real Application Testing options

---- Connect to root container


[oracle@localhost ~]$ rman target sys/oracle@cdb1

Recovery Manager: Release 12.1.0.2.0 - Production on Fri Aug 28 22:46:04 2015

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

connected to target database: CDB1 (DBID=828012650)



RMAN> backup database plus archivelog
2> ;


Starting backup at 28-AUG-15
current log archived
using target database control file instead of recovery catalog
allocated channel: ORA_DISK_1
channel ORA_DISK_1: SID=30 device type=DISK
channel ORA_DISK_1: starting archived log backup set
channel ORA_DISK_1: specifying archived log(s) in backup set
input archived log thread=1 sequence=165 RECID=1 STAMP=886318673
input archived log thread=1 sequence=166 RECID=2 STAMP=886319099
input archived log thread=1 sequence=167 RECID=3 STAMP=886320315
input archived log thread=1 sequence=168 RECID=4 STAMP=886321194

channel ORA_DISK_1: finished piece 1 at 28-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/backupset/2015_08_28/o1_mf_annnn_TAG20150828T224727_by2kxold_.bkp tag=TAG20150828T224727 comment=NONE
channel ORA_DISK_1: backup set complete, elapsed time: 00:00:56
Finished backup at 28-AUG-15

Starting backup at 28-AUG-15
using channel ORA_DISK_1
channel ORA_DISK_1: starting full datafile backup set
channel ORA_DISK_1: specifying datafile(s) in backup set
input datafile file number=00031 name=/home/oracle/app/oracle/oradata/cdb1/testencry.dbf
input datafile file number=00003 name=/home/oracle/app/oracle/oradata/cdb1/sysaux01.dbf
input datafile file number=00001 name=/home/oracle/app/oracle/oradata/cdb1/system01.dbf
input datafile file number=00004 name=/home/oracle/app/oracle/oradata/cdb1/undotbs01.dbf
input datafile file number=00034 name=/home/oracle/app/oracle/oradata/cdb1/dataconversion.dbf
input datafile file number=00037 name=/home/oracle/app/oracle/oradata/cdb1/testin1.dbf
input datafile file number=00006 name=/home/oracle/app/oracle/oradata/cdb1/users01.dbf
channel ORA_DISK_1: starting piece 1 at 28-AUG-15

Starting backup at 28-AUG-15
current log archived
using channel ORA_DISK_1
channel ORA_DISK_1: starting archived log backup set
channel ORA_DISK_1: specifying archived log(s) in backup set
input archived log thread=1 sequence=268 RECID=104 STAMP=888965884
channel ORA_DISK_1: starting piece 1 at 28-AUG-15
channel ORA_DISK_1: finished piece 1 at 28-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/backupset/2015_08_28/o1_mf_annnn_TAG20150828T225804_by2lhdwl_.bkp tag=TAG20150828T225804 comment=NONE
channel ORA_DISK_1: backup set complete, elapsed time: 00:00:01
Finished backup at 28-AUG-15

Starting Control File and SPFILE Autobackup at 28-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/autobackup/2015_08_28/o1_mf_s_888965886_by2lhhc8_.bkp comment=NONE
Finished Control File and SPFILE Autobackup at 28-AUG-15

Taking backup of particular pluggable database:(backup pluggable database ORCL;)
---- Connect to root container



[oracle@localhost ~]$ rman target sys/oracle@cdb1

Recovery Manager: Release 12.1.0.2.0 - Production on Fri Aug 28 22:46:04 2015

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

connected to target database: CDB1 (DBID=828012650)



RMAN> backup pluggable database ORCL;

Starting backup at 28-AUG-15
using target database control file instead of recovery catalog
allocated channel: ORA_DISK_1
channel ORA_DISK_1: SID=12 device type=DISK
channel ORA_DISK_1: starting full datafile backup set
channel ORA_DISK_1: specifying datafile(s) in backup set
input datafile file number=00008 name=/home/oracle/app/oracle/oradata/cdb1/orcl/system01.dbf
input datafile file number=00011 name=/home/oracle/app/oracle/oradata/cdb1/orcl/example01.dbf
input datafile file number=00009 name=/home/oracle/app/oracle/oradata/cdb1/orcl/sysaux01.dbf
input datafile file number=00010 name=/home/oracle/app/oracle/oradata/cdb1/orcl/SAMPLE_SCHEMA_users01.dbf
channel ORA_DISK_1: specifying datafile(s) in backup set
input datafile file number=00008 name=/home/oracle/app/oracle/oradata/cdb1/orcl/system01.dbf
input datafile file number=00011 name=/home/oracle/app/oracle/oradata/cdb1/orcl/example01.dbf
input datafile file number=00009 name=/home/oracle/app/oracle/oradata/cdb1/orcl/sysaux01.dbf
input datafile file number=00010 name=/home/oracle/app/oracle/oradata/cdb1/orcl/SAMPLE_SCHEMA_users01.dbf
input datafile file number=00033 name=/home/oracle/app/oracle/oradata/cdb1/orcl/dataconversion.dbf
input datafile file number=00023 name=/home/oracle/app/oracle/oradata/cdb1/orcl/APEX_3496321052328731.dbf
input datafile file number=00027 name=/home/oracle/app/oracle/oradata/cdb1/orcl/APEX_3638406606618093.dbf
input datafile file number=00029 name=/home/oracle/app/oracle/oradata/cdb1/orcl/APEX_1780406307370394.dbf
input datafile file number=00028 name=/home/oracle/app/oracle/oradata/cdb1/orcl/APEX_3753603687620385.dbf
input datafile file number=00030 name=/home/oracle/app/oracle/oradata/cdb1/orcl/APEX_5372044460374154.dbf
input datafile file number=00024 name=/home/oracle/app/oracle/oradata/cdb1/orcl/APEX_3618122143496338.dbf
input datafile file number=00025 name=/home/oracle/app/oracle/oradata/cdb1/orcl/APEX_3624405313851440.dbf
input datafile file number=00026 name=/home/oracle/app/oracle/oradata/cdb1/orcl/APEX_3632418306476203.dbf
channel ORA_DISK_1: starting piece 1 at 28-AUG-15
channel ORA_DISK_1: finished piece 1 at 28-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/FF72AA85A0370D5BE045000000000001/backupset/2015_08_28/o1_mf_nnndf_TAG20150828T232125_by2mv65d_.bkp tag=TAG20150828T232125 comment=NONE
channel ORA_DISK_1: backup set complete, elapsed time: 00:01:15
Finished backup at 28-AUG-15

Starting Control File and SPFILE Autobackup at 28-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/autobackup/2015_08_28/o1_mf_s_888967361_by2mxlpf_.bkp comment=NONE
Finished Control File and SPFILE Autobackup at 28-AUG-15



channel ORA_DISK_1: starting piece 1 at 28-AUG-15

Backup of only root container:
RMAN> backup database root
2> ;

Starting backup at 29-AUG-15
using channel ORA_DISK_1
channel ORA_DISK_1: starting full datafile backup set
channel ORA_DISK_1: specifying datafile(s) in backup set
input datafile file number=00031 name=/home/oracle/app/oracle/oradata/cdb1/testencry.dbf
input datafile file number=00003 name=/home/oracle/app/oracle/oradata/cdb1/sysaux01.dbf
input datafile file number=00001 name=/home/oracle/app/oracle/oradata/cdb1/system01.dbf
input datafile file number=00004 name=/home/oracle/app/oracle/oradata/cdb1/undotbs01.dbf
input datafile file number=00034 name=/home/oracle/app/oracle/oradata/cdb1/dataconversion.dbf
input datafile file number=00037 name=/home/oracle/app/oracle/oradata/cdb1/testin1.dbf
input datafile file number=00006 name=/home/oracle/app/oracle/oradata/cdb1/users01.dbf
channel ORA_DISK_1: starting piece 1 at 29-AUG-15





channel ORA_DISK_1: finished piece 1 at 29-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/backupset/2015_08_29/o1_mf_nnndf_TAG20150829T010145_by2sqbd9_.bkp tag=TAG20150829T010145 comment=NONE
channel ORA_DISK_1: backup set complete, elapsed time: 00:01:25
Finished backup at 29-AUG-15

Starting Control File and SPFILE Autobackup at 29-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/autobackup/2015_08_29/o1_mf_s_888973391_by2sszjo_.bkp comment=NONE
Finished Control File and SPFILE Autobackup at 29-AUG-15

Backup of tablespace of pluggable database(by connecting to PDB )
[oracle@localhost admin]$ rman target=sys@ORCL

Recovery Manager: Release 12.1.0.2.0 - Production on Sat Aug 29 01:12:28 2015

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

target database Password: 
connected to target database: CDB1 (DBID=828012650)


RMAN> backup tablespace USERS;

Starting backup at 29-AUG-15
using channel ORA_DISK_1
channel ORA_DISK_1: starting full datafile backup set
channel ORA_DISK_1: specifying datafile(s) in backup set
input datafile file number=00010 name=/home/oracle/app/oracle/oradata/cdb1/orcl/SAMPLE_SCHEMA_users01.dbf
channel ORA_DISK_1: starting piece 1 at 29-AUG-15
channel ORA_DISK_1: finished piece 1 at 29-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/FF72AA85A0370D5BE045000000000001/backupset/2015_08_29/o1_mf_nnndf_TAG20150829T011323_by2tf3vl_.bkp tag=TAG20150829T011323 comment=NONE
channel ORA_DISK_1: backup set complete, elapsed time: 00:00:07
Finished backup at 29-AUG-15

Starting Control File and SPFILE Autobackup at 29-AUG-15
piece handle=/home/oracle/app/oracle/fast_recovery_area/CDB1/autobackup/2015_08_29/o1_mf_s_888974011_by2tfcd3_.bkp comment=NONE
Finished Control File and SPFILE Autobackup at 29-AUG-15