Very good and fun set-up, Boratz! I haven't seen Bulletproof Monk, but this story definitely feels a good deal like the Relic Hunter episodes I remember seeing.
As for the match, while Sydney is a pretty good fighter, as mentioned I do seem to remember her losing her share of fights as well. Looking at a clip from Bulletproof Monk, Nina's attacks seem a little crisper than Sydney's. Given that and the facts that Nina is younger and Sydney's likely at least a bit past her prime, I think Nina wins after a fairly tough fight, leaving Claudia on her own to retrieve Brutus's dagger.