Well the animation will not likely be there.
As elasticity is a defense and that seems to be primary in your concept
I would go for a STALWART. defense primary and melee secondary.

I would go for Protection power sets, Invulnerability or Solid Form

So you want something resilient, it doesn't fight the damage but snaps back quickly. A method of attack that's flexible.

If this were CoH, I'd be suggesting Regeneration or Willpower and Kinetic Melee or perhaps Dual Blades. Unfortunately, we don't (yet) know enough about the powerset mechanics in CoT to make concrete suggestions, in my opinion. Add to that the way that Aesthetic Decoupling will give us the ability to make many things Look like practically anything else...

Still, with a name like 'Escapade', I could see tricks and traps and tools, a Staff, or some form of melee-touch Confusion/Control, on top of the physical resilience to survive a beating. Possibly even a damage 'absorption' powerset, where the more bombs you throw at her, the more she laughs. If we had a 'Grappling' or Physical Control set, that might work, too.

Myself, I'm looking forward to the Stalwart>Centurion AT, depending on how much 'control' the promised 'Manipulation' powersets give. You might be attracted to the Enforcer>Striker, with its Melee/Manipulation sets.

Be Well!
Fireheart

Let me assume that the animation for an unbreakable rubber character will not exist. So we have to make a simulation. A proper simulation would be one that allows itself to get hit, but which reduces the damage received significantly because physical attacks just don't hurt.

There really is only one choice to simulate this: Invulnerability.

From a simulation point of view, it reproduces the effects you are looking for. Resistance to physical damage types, but less resistance to energy and exotic damage types.

And since you made no mention of any offensive powers, she will be a Stalwart Archetype with the Invulnerability Primary Power Set.

Secondary Power Set (aka Specialization) would probably be the Fighting Prowess melee set. Because every attack you make reduces the damage you receive. Again, this plays upon the invulnerability concept of the rubber body.

so... what about an Invulnrability/ fighting prowess? Invulnrability can reduce a lot of damage just like rubber, and prowess gives you defense and the riposte power which states that any attack that misses you gets afflicted on the one who attacked you, so you have plenty of opportunity to resist damage and send it back.