The standard is vague. The Constitution says officials can be impeached for “high crimes and misdemeanors,” but doesn’t define that term. So, it largely means whatever the House and Senate say it means.
Historically, judges have been impeached for a variety of reasons — from showing up to work drunk, to joining the Confederacy, to accepting bribes.
But, according to a 2015 report from the Congressional Research Service, no one has ever been impeached “solely on the basis of conduct occurring before he began his tenure in the office held at the time of the impeachment investigation” — as would be the case if Kavanaugh were impeached over anything that has already happened, including his confirmation hearing.