After discovering what happened to Mel and Owen, you’ll find yourself at the Theatre. Here you’ll want to go around to the right and climb up the ladder to gain access. Once you’re inside, go downstairs for a cutscene, then chase Ellie into the backstage area.
In order to win this fight you’ll want to sneak around and wait until Ellie turns her back then strike. Upon falling down to the lower floor you’ll want to quickly dodge Ellie’s shotgun shot, then sneak around the area again until you see another opening.
However, make sure to watch your surroundings as you can step on glass which will alert Ellie to your position or you may step on one of Ellie’s Trap Mines that she planted. Upon successfully striking Ellie twice a cutscene will play out.