Dodge Greek character beginning to get extremely greedy, the muppet! (4,5)
I believe the answer is:
miss piggy
'muppet' is the definition.
I know nothing about this answer so I can't judge whether this works.
'dodge greek character beginning to get extremely greedy' is the wordplay.
'dodge' becomes 'miss' (I can't justify this - if you can you should believe this answer much more).
'greek character' becomes 'pi' (letter from the Greek alphabet).
'beginning to' says to take the initial letters.
'extremely' means to remove the middle letters (letters on the extremes of the word are used).
'greedy' with its centre removed is 'gy'.
The first letter of 'get' is 'g'.
'miss'+'pi'+'g'+'gy'='MISS PIGGY'
'the' is the link.
Can you help me to learn more?