Oh, it doesn't take long at all. It just involves leading his ass up the stairs and blasting him in the back three times until he turns towards you. ...Of course since you'll be behind him on the second level while he's still climbing the stairs he'll just be dashing towards the railing before turning around and trying to go up the stairs again. Of course, you'll have to initiate Wesker kicking you through a door first so Jill doesn't murder your ass while you're trying it.
Rinse, Repeat and done. I beat him in like under a minute with this strategy and it's how I got the Heart of Africa.