When it comes to cooking, I won't lose to anyone.

Literal

Cooking [possessive-の] matter [if-であれば], anyone [to-にも] won't-lose [emphasis-よ].

~のことであれば is a conditional meaning 'if it's a matter of X' or 'when it comes to X.' 誰にも負けない (won't lose to anyone) is a strong self-assertion — にも makes it emphatic. The sentence-final よ adds assertive force.