The same qualities that make a good hero, only in reverse order.
The thing is, if you want a really great anti-hero, you must make that character believable, easy to hate, and easy to love.
So the qualities that make a good anti-hero don’t depend as much on what the qualities are as they do on what percentage of each quality the anti-hero possesses.
Give him more of what you want readers to hate, less of what you want them to love and enough quirks to make him human.
But they must all be there.