To be snakelike was Hitler's undoing (7)

I believe the answer is:

slither

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'to be snakelike' is the definition.
I can't tell whether this defines the answer.

'hitler's undoing' is the wordplay.
'undoing' indicates an anagram.
'hitlers' with letters rearranged gives 'SLITHER'.

'was' acts as a link.

Can you help me to learn more?

(Other definitions for slither that I've seen before include "Snake along" , "Quietly advance" , "Slide (like a snake)" , "Slide on slippery surface" , "Move like a snake" .)

I've seen this clue in the Evening Standard.

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