"Insufficient privileges" while shutting down as sysoper
It depends upon how you have granted the SYSOPER privilege. To shutdown the database instance user should have SYSOPER privilege on all containers.

The following demonstrate the scenario.

I have common user call C##_TEST.

[oracle@ora12c dbs]$ sqlplus sys@oracdb as sysdba

SQL*Plus: Release 12.1.0.2.0 Production on Fri Dec 2 08:47:05 2016

Copyright (c) 1982, 2014, Oracle.  All rights reserved.

Enter password: 

Connected to:
Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
With the Partitioning, Automatic Storage Management, OLAP, Advanced Analytics
and Real Application Testing options


SQL&gt; select common from dba_users where username='C##_TEST';

COM
---
YES


I have granted SYSOPER to the user for the ORACDB(CDB) only.

SQL&gt; grant sysoper to c##_test container=current;

Grant succeeded.


Then I have connected to container database using C##_TEST user as SYSOPER and tried to shut down the database and got the ORA-01031 error.

[oracle@ora12c dbs]$ sqlplus c##_test/test@oracdb as sysoper

SQL*Plus: Release 12.1.0.2.0 Production on Fri Dec 2 08:49:05 2016

Copyright (c) 1982, 2014, Oracle.  All rights reserved.


Connected to:
Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
With the Partitioning, Automatic Storage Management, OLAP, Advanced Analytics
and Real Application Testing options

SQL&gt; shut immediate;
ORA-01031: insufficient privileges
SQL&gt; 


Now I again granted the SYSOPER privilege with the option container=all. And this time the user can shut down the database.

[oracle@ora12c dbs]$ sqlplus sys@oracdb as sysdba

SQL*Plus: Release 12.1.0.2.0 Production on Fri Dec 2 08:49:36 2016

Copyright (c) 1982, 2014, Oracle.  All rights reserved.

Enter password: 

Connected to:
Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
With the Partitioning, Automatic Storage Management, OLAP, Advanced Analytics
and Real Application Testing options

SQL&gt; grant sysoper to c##_test container=all;

Grant succeeded.

SQL&gt; exit
Disconnected from Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
With the Partitioning, Automatic Storage Management, OLAP, Advanced Analytics
and Real Application Testing options

[oracle@ora12c dbs]$ sqlplus c##_test/test@oracdb as sysoper

SQL*Plus: Release 12.1.0.2.0 Production on Fri Dec 2 08:50:06 2016

Copyright (c) 1982, 2014, Oracle.  All rights reserved.


Connected to:
Oracle Database 12c Enterprise Edition Release 12.1.0.2.0 - 64bit Production
With the Partitioning, Automatic Storage Management, OLAP, Advanced Analytics
and Real Application Testing options

SQL&gt; shut immediate;
Database closed.
Database dismounted.
ORACLE instance shut down.