It has to be at least as strong as Zeus' master bolt. [ Poseidon's trident, the helm of Hades, etc etc. ] Don't forget about the shield. Rachel's prophecy made it pretty clear that the sword isn't the only important part.

[ of course she didn't foresee the mirrors bleeding into real side and getting a chance to try to win the sword with their own merits. ]

I know, and she's trying. She's going to get it. She just needs more time.