The leader of AVALANCHE is no pushover. He showed this last week in his pummeling of one of those @#$%ing Shinra employees, and he'll show it again this week. Eileen is a highly-thought of Middle? Well, Barret didn't ask for no easy fights. Invincibility's a pretty fancy trick, but it'd be fancier if it didn't guard against instant death, something Barret has access to through his infamous Hammerblow. One shot of that will send Eileen hella far, regardless of whatever metals she can coat her skin with. And with the impressive durability you'd expect of someone as muscular and determined as Barret @#$%ing Wallace, avoiding his limit breaks is not something many Middles can claim to be able to do.