Many cheer evil foe (4-5)

I believe the answer is:

arch-enemy

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'foe' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.

'many cheer evil' is the wordplay.
'evil' is an anagram indicator.
'many'+'cheer'='manycheer'
'manycheer' anagrammed gives 'ARCH-ENEMY'.

Can you help me to learn more?

(Another definition for arch-enemy that I've seen is " Principal antagonist".)

I've seen this clue in The Telegraph.

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