to save one's life
Even if one's life depended on it, as in I couldn't eat another bite to save my life, or Betty wouldn't climb a mountain to save her life. This hyperbolic expression nearly always follows a negative statement that one wouldn't or couldn't do something. Anthony Trollope used a slightly different wording in The Kellys and the O'Kellys (1848): “I shan't remain long, if it was to save my life and theirs; I can't get up small talk for the rector and his curate.”
Words nearby to save one's life
to one's name,
to oneself,
to order,
to pieces,
to rights,
to save one's life,
to say nothing of,
to say the least,
to some degree,
to spare,
to speak of