No need to make fun of such desperate pleas for demise (4-9)

I believe the answer is:

self-parodying

I'm a little stuck... Click here to teach me more about this clue!

'no need to make fun of' is the definition.
I can't judge whether this definition defines the answer.

'desperate pleas for demise' is the wordplay.
'desperate' indicates anagramming the letters (a desperate or pathetic spelling).
'demise' becomes 'dying' (synonyms).
'pleas'+'for'='pleasfor'
'pleasfor' is an anagram of 'selfparo'.
'selfparo'+'dying'='SELF-PARODYING'

'such' acts as a link.

Can you help me to learn more?

I've seen this clue in The Guardian.

Want a hint initially instead of a full solution? Install my app