Regarding whether or not the harpoon could damage Bubbles.
Presumably as a military grade chassis, Bubbles' dermal layers can withstand up to a .500 Magnum, which is the most powerful production handgun round at the moment. So presumably Bubbles' dermal layers work on the same premise that all bullet resistant technology works, multiple layers that work to slow a bullet and forcing it to expend its energy to the point where it can no longer continue. This works because the instant a bullet is fired, its already expending kinetic energy, slowing down the further it has to travel. Bullet resistant technology capitalises on that, having layers of material that disperses impact energy over a wider area, which in turn forces the bullet to expend even more kinetic energy to pierce another layer until its stopped.
That said, bullet resistant doesn't mean stab resistant. Dependant on the materials used, a stabbing weapon will enter slower than a bullet and unless there was a tighter weave, would simply cut through the layers. This is because as I pointed out, a bullet is slowing down the instant it is fired, whereas a knife (or in this case a harpoon) will have a consistent and considerable amount of force behind it (again, in this case Brun). Essentially you're (relatively, you're talking a difference of around half a second) slowly cutting through layers.
So, unless Bubbles's has different kinds of Kevlar under her skin, she might want to be careful of that harpoon.