Doing everything possible to be irritating? (6,4,7)

I believe the answer is:

trying ones hardest

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

'doing everything possible' is the definition.
I can't tell whether this defines the answer.

'be irritating?' is the wordplay.
I cannot quite see how this works, but
'be' could be 'go' (going is a kind of being) and 'go' is found in the answer.
This may be the basis of the clue (or it may be nonsense).

'to' acts as a link.

Can you help me to learn more?

I've seen this clue in the Evening Standard.

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