How to  correctly purge old RMAN backups when storage runs out of space 

Do not use rm to remove files 

as I did this blunder once and got escalated :P

You must do it via RMAN.

$ export NLS_DATE_FORMAT='DD-MM-YY HH24:MI'

$ rman target / NOCATALOG

RMAN > crosscheck backupset;
This command will verify whether backup file is still on media.
If it is unavailable, RMAN will mark it as UNAVAILABLE or EXPIRED.

RAMN > delete expired backupset;
or
RMAN > delete expired backup;

Note : If you manually rename or zip RMAN backup files, 
you must manually remove it from disk since RMAN
does not recognize them.

RMAN > report obsolete;

The command lists all backups rendered obsolete based on rentention policy.
Current Retention Policy is 'Recovery WINDOW OF 30 DAYS'.

RMAN > delete obsolete;

RMAN > list backup summary;
It will show all backupset info kept in RMAN repository.
If you want to see what RMAN keeps in each backupset, 

run 'list backupset N' where N is Backupset ID.

RMAN > delete backupset N;
or
RMAN > delete backupset; (to delete all backups)

Once fair amount of space is reclaimed, do full backup.
Not sure how much full back space is needed but not less than 20G.

RMAN > backup database;

RMAN > list backup;
Full backup may have more than one backupset.
Look for last backupsets. It will list backup db files.

RMAN > delete obsolete;
Rerun this command to delete unwanted existing backupsets
 (if have) after completed full backup.